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## Texas Go Math Grade 3 Lesson 3.1 Answer Key Compare Fractions with the Same Denominator

**Essential Question
**How can you compare fractions with the same denominator?

Answer:

When the denominators are the same, the fraction with the lesser numerator is the lesser fraction and the fraction with the greater numerator is the greater fraction. When the numerators are equal, the fractions are considered equivalent

**Unlock the problem**

Jeremy and Christina are each making a quilt block. Both blocks are the same size and both are made of 4 equal-size squares. \(\frac{2}{4}\) of Jeremy’s squares are green. \(\frac{1}{4}\) of Christina’s squares are green. Whose quilt block has more green squares?

• Circle the two fractions you need to compare.

Answer:

The two fractions that you need to compare are:

\(\frac{2}{4}\) and \(\frac{1}{4}\)

• How are the two fractions alike?

Answer:

The two fractions have the same denominator but different numerators

Compare fractions of a whole.

- Shade \(\frac{2}{4}\) of Jeremy’s quilt block.
- Shade \(\frac{1}{4}\) of Christina’s quilt block.
- Compare the shaded parts.

\(\frac{2}{4}\) > \(\frac{1}{4}\)

The greater fraction will have the larger amount of the whole shaded.

So,

Jeremy’s quilt block has more green squares.

**Math Idea**

You can compare two fractions when they refer to the same whole or to groups that are the same size.

Compare fractions of a group.

Jen and Maggie each have 6 buttons.

• Shade 3 of Jen’s buttons to show the number of buttons that are red. Shade 5 of Maggie’s buttons to show the number that is red.

• Write a fraction to show the number of red buttons in each group. Compare the fractions.

The fraction of the number of Jen’s red buttons = \(\frac{3}{6}\)

The fraction of the number of Maggie’s red buttons = \(\frac{5}{6}\)

There is the same number of buttons in each group, so you can count the number of red buttons to compare the fractions.

So,

Maggie has a greater fraction of red buttons.

**Use fraction strips and a number line.**

At the craft store, one piece of ribbon is \(\frac{2}{8}\) yard long. Another piece of ribbon is \(\frac{7}{8}\) yard long. Which piece of ribbon is longer?

Compare \(\frac{2}{8}\) and \(\frac{7}{8}\).

- Shade the fraction strip diagrams to show the locations of \(\frac{2}{8}\) and \(\frac{7}{8}\).

- Draw and label the points on the number line.

- Compare the lengths.

**Share and Show**

Question 1.

Draw points on the number line to show \(\frac{1}{6}\) and \(\frac{5}{6}\). Then compare the fractions.

Answer:

The given number line is:

Now,

When we observe the given number line,

\(\frac{1}{6}\) is to the left of \(\frac{5}{6}\)

The denominators are the same

So,

Compare the numerators

Hence, from the above

We can conclude that

**Math Talk**

**Mathematical Processes**

Explain why fractions increase in size as you move right on the number line.

Answer:

A number line is a way to see the size of numbers by placing them along a line. A number line is usually horizontal with zero in the middle. As you move to the right the numbers are positive and increase. As you go to the left, the numbers also increase and get more and more negative.

**Compare. Write <, >, or =.**

Question 2.

\(\frac{4}{8}\) \(\frac{3}{8}\)

Answer:

The given fractions are:

\(\frac{4}{8}\) and \(\frac{3}{8}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

So,

4 > 3

Hence, from the above,

We can conclude that

Question 3.

\(\frac{1}{4}\) \(\frac{4}{4}\)

Answer:

The given fractions are:

\(\frac{1}{4}\) and \(\frac{4}{4}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

So,

1 < 4

Hence, from the above,

We can conclude that

Question 4.

\(\frac{1}{2}\) \(\frac{1}{2}\)

Answer:

The given fractions are:

\(\frac{1}{2}\) and \(\frac{1}{2}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

So,

1 = 1

Hence, from the above,

We can conclude that

Question 5.

\(\frac{3}{6}\) \(\frac{2}{6}\)

Answer:

The given fractions are:

\(\frac{3}{6}\) and \(\frac{2}{6}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

So,

3 > 2

Hence, from the above,

We can conclude that

**Problem Solving**

Question 6.

Carlos finished \(\frac{5}{8}\) of his art project on Monday. Tyler finished \(\frac{7}{8}\) of his art project on Monday. Who finished more of his art project on Monday?

Answer:

It is given that

Carlos finished \(\frac{5}{8}\) of his art project on Monday. Tyler finished \(\frac{7}{8}\) of his art project on Monday

Now,

The given fractions are:

\(\frac{5}{8}\) and \(\frac{7}{8}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

So,

5 < 7

So,

\(\frac{5}{8}\) < \(\frac{7}{8}\)

Hence, from the above,

We can conclude that

Tyler finished more of his art project on Monday

Question 7.

Mallory picked 4 roses for her mother. One-fourth of the roses are pink and \(\frac{3}{4}\) of the roses are red. Are there more pink roses or red roses?

Answer:

It is given that

Mallory picked 4 roses for her mother. One-fourth of the roses are pink and \(\frac{3}{4}\) of the roses are red

So,

The fraction of the roses that are pink = \(\frac{1}{4}\)

Now,

The given fractions are:

\(\frac{1}{4}\) and \(\frac{3}{4}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

So,

1 < 3

So,

\(\frac{1}{4}\) < \(\frac{3}{4}\)

Hence, from the above,

We can conclude that

There are more red roses

Question 8.

**Use Tools Multi-Step** Lauren ran \(\frac{7}{8}\) of a mile in a race. Jacob ran \(\frac{5}{8}\) of a mile. Draw points on the number line to show \(\frac{7}{8}\) and \(\frac{5}{8}\). Then compare the fractions.

Answer:

It is given that

Lauren ran \(\frac{7}{8}\) of a mile in a race. Jacob ran \(\frac{5}{8}\) of a mile

Now,

The given number line is:

Now,

The representation of the number of miles on the given number line is:

Now,

The given fractions are:

\(\frac{5}{8}\) and \(\frac{7}{8}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

So,

5 < 7

So,

\(\frac{5}{8}\) < \(\frac{7}{8}\)

Hence, from the above,

We can conclude that

Question 9.

**H.O.T. What’s the Error?** Gary and Vanessa are comparing fractions. Vanessa models \(\frac{2}{4}\) and Gary models \(\frac{3}{4}\). Vanessa writes \(\frac{3}{4}\) < \(\frac{2}{4}\). Look at Gary’s model and Vanessa’s model and find her error.

**Multi-Step** Describe Vanessa’s error and explain how to correct it.

Answer:

It is given that

Gary and Vanessa are comparing fractions. Vanessa models \(\frac{2}{4}\) and Gary models \(\frac{3}{4}\). Vanessa writes \(\frac{3}{4}\) < \(\frac{2}{4}\)

Now,

The given models are:

Now,

From the above models,

We can observe that

The total number of parts is the same

The number of shaded parts is different

Now,

The given fractions are:

\(\frac{2}{4}\) and \(\frac{3}{4}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

So,

2 < 3

So,

\(\frac{2}{4}\) < \(\frac{3}{4}\)

Hence, from the above,

We can conclude that

Vanessa’s error is: The incorrect counting of the number of shaded boxes

The correct comparison is:

\(\frac{2}{4}\) < \(\frac{3}{4}\)

**Daily Assessment Task**

**Use fraction strips to compare. Fill in the bubble for the correct answer choice.**

Question 10.

At a car show, \(\frac{4}{8}\) of the cars are red. A smaller fraction of the cars is black. Which could be the fraction of the cars that are black?

(A) \(\frac{4}{8}\)

(B) \(\frac{2}{8}\)

(C) \(\frac{8}{8}\)

(D) \(\frac{6}{8}\)

Answer:

It is given that

At a car show, \(\frac{4}{8}\) of the cars are red. A smaller fraction of the cars is black.

Now,

Let the total number of cars be: 1

So,

(The fraction of cars that are red) + (The fraction of cars that are black) = 1

So,

The number of cars that are black = 1 – \(\frac{4}{8}\)

= \(\frac{8 – 4}{8}\)

= \(\frac{4}{8}\)

Hence, from the above,

We can conclude that

The fraction of the cars that are black are:

Question 11.

Which fraction makes the statement true?

(A) \(\frac{3}{6}\)

(B) \(\frac{2}{6}\)

(C) \(\frac{5}{6}\)

(D) \(\frac{1}{6}\)

Answer:

The given fraction is:

\(\frac{2}{6}\)

Now,

We know that,

If the denominators are the same, compare the numerators

Hence, from the above,

We can conclude that

The fraction that makes the given statement true is:

Question 12.

**Apply Multi-Step** There are two same-size scarves. Jo’s scarf is divided into 4 equal sections. Three of the sections are blue. A greater fraction of Morgan’s scarf is blue. Which could be the fraction of Morgan’s scarf that is blue?

(A) \(\frac{4}{4}\)

(B) \(\frac{2}{4}\)

(C) \(\frac{1}{4}\)

(D) \(\frac{3}{4}\)

Answer:

It is given that

There are two same-size scarves. Jo’s scarf is divided into 4 equal sections. Three of the sections are blue. A greater fraction of Morgan’s scarf is blue

Now,

According to the given information,

The fraction of Morgan’s scarf that is blue = (The number of sections that are shaded blue) ÷ (The total number of sections)

= \(\frac{3}{4}\)

Hence, from the above,

We can conclude that

The fraction of Morgan’s scarf that is blue is:

**Texas Test Prep**

Question 13.

Todd and Lisa are comparing fraction strips. Which statement is NOT correct?

(A) \(\frac{1}{4}\) < \(\frac{4}{4}\)

(B) \(\frac{5}{6}\) < \(\frac{4}{6}\) (C) \(\frac{2}{3}\) > \(\frac{1}{3}\)

(D) \(\frac{5}{8}\) > \(\frac{4}{8}\)

Answer:

It is given that

Todd and Lisa are comparing fraction strips

Hence, from the above,

We can conclude that

The statement that is not correct is:

### Texas Go Math Grade 3 Lesson 3.1 Homework and Practice Answer Key

**Compare. Write <, >, or =.**

Question 1.

\(\frac{5}{8}\) \(\frac{4}{8}\)

Answer:

The given fractions are:

\(\frac{5}{8}\) and \(\frac{4}{8}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

So,

5 > 4

Hence, from the above,

We can conclude that

Question 2.

\(\frac{1}{4}\) \(\frac{4}{4}\)

Answer:

The given fractions are:

\(\frac{1}{4}\) and \(\frac{4}{4}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

So,

1 < 4

Hence, from the above,

We can conclude that

Question 3.

\(\frac{1}{6}\) \(\frac{2}{6}\)

Answer:

The given fractions are:

\(\frac{1}{6}\) and \(\frac{2}{6}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

So,

1 < 2

Hence, from the above,

We can conclude that

Question 4.

\(\frac{2}{3}\) \(\frac{1}{3}\)

Answer:

The given fractions are:

\(\frac{2}{3}\) and \(\frac{1}{3}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

So,

2 > 1

Hence, from the above,

We can conclude that

Question 5.

\(\frac{1}{2}\) \(\frac{0}{2}\)

Answer:

The given fractions are:

\(\frac{1}{2}\) and \(\frac{0}{2}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

So,

1 > 0

Hence, from the above,

We can conclude that

Question 6.

\(\frac{7}{8}\) \(\frac{6}{8}\)

Answer:

The given fractions are:

\(\frac{7}{8}\) and \(\frac{6}{8}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

So,

7 > 6

Hence, from the above,

We can conclude that

Question 7.

\(\frac{5}{6}\) \(\frac{5}{6}\)

Answer:

The given fractions are:

\(\frac{5}{6}\) and \(\frac{5}{6}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

So,

5 = 5

Hence, from the above,

We can conclude that

Question 8.

\(\frac{1}{3}\) \(\frac{3}{3}\)

Answer:

The given fractions are:

\(\frac{1}{3}\) and \(\frac{3}{3}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

So,

1 < 3

Hence, from the above,

We can conclude that

**Problem Solving**

Question 9.

Greg finished \(\frac{3}{8}\) of his chores on Saturday and \(\frac{5}{8}\) of his chores on Sunday. On which day did he finish fewer chores?

Answer:

It is given that

Greg finished \(\frac{3}{8}\) of his chores on Saturday and \(\frac{5}{8}\) of his chores on Sunday

Now,

The given fractions are:

\(\frac{3}{8}\) and \(\frac{5}{8}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

So,

3 < 5

So,

\(\frac{3}{8}\) < \(\frac{5}{8}\)

Hence, from the above,

We can conclude that

Greg finished the least chores on Saturday

Question 10.

Tia completed \(\frac{3}{6}\) of her math homework problems before dinner. After dinner, she finished \(\frac{3}{6}\) of the problems. Did she do more problems before or after dinner?

Answer:

It is given that

Tia completed \(\frac{3}{6}\) of her math homework problems before dinner. After dinner, she finished \(\frac{3}{6}\) of the problems

Now,

The given fractions are:

\(\frac{3}{6}\) and \(\frac{3}{6}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

So,

3 = 3

So,

\(\frac{3}{6}\) = \(\frac{3}{6}\)

Hence, from the above,

We can conclude that

Tia did the same problems before and after dinner

**Texas test Prep**

**Lesson Check**

**Fill in the bubble completely to show your answer.**

Question 11.

Which fraction makes the statement true?

(A) \(\frac{7}{8}\)

(B) \(\frac{5}{8}\)

(C) \(\frac{2}{8}\)

(D) \(\frac{4}{8}\)

Answer:

The given fraction is:

\(\frac{3}{8}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

Hence, from the above,

We can conclude that

The fraction that makes the given statement true is:

Question 12.

Which fraction makes the statement true?

(A) \(\frac{1}{6}\)

(B) \(\frac{3}{6}\)

(C) \(\frac{5}{6}\)

(D) \(\frac{2}{6}\)

Answer:

The given fraction is:

\(\frac{3}{6}\)

Now,

We know that,

If the denominators are the same, then compare the numerators

Hence, from the above,

We can conclude that

The fraction that makes the given statement true is:

Question 13.

In a fish tank, \(\frac{5}{8}\) of the fish are yellow. A smaller fraction of the fish is blue. Which could be the fraction of the fish that are blue?

(A) \(\frac{3}{8}\)

(B) \(\frac{6}{8}\)

(C) \(\frac{8}{8}\)

(D) \(\frac{5}{8}\)

Answer:

It is given that

In a fish tank, \(\frac{5}{8}\) of the fish are yellow. A smaller fraction of the fish is blue

Now,

Let the total number of fish in a fish tank be: 1

So,

(The fraction of the fish that are yellow) + (The fraction of the fish that are blue) = 1

So,

The fraction of the fish that are blue = 1 – \(\frac{5}{8}\)

= \(\frac{8 – 5}{8}\)

= \(\frac{3}{8}\)

Hence, from the above,

We can conclude that

The fraction of the fish that is blue is:

Question 14.

Wes collects sports cards. In his collection, \(\frac{3}{6}\) of the cards are baseball cards. A smaller fraction of the cards is football cards. Which could be the fraction of the cards that are football cards?

Answer:

It is given that

Wes collects sports cards. In his collection, \(\frac{3}{6}\) of the cards are baseball cards. A smaller fraction of the cards is football cards

Now,

Let the total number of sports cards be: 1

So,

(The fraction of the cards that is baseball cards) + (The fraction of the cards that is football cards) = 1

So,

The fraction of the cards that is football cards = 1 – \(\frac{3}{6}\)

= \(\frac{6 – 3}{6}\)

= \(\frac{3}{6}\)

Hence, from the above,

We can conclude that

The fraction of the cards that is football cards is:

Question 15.

**Multi-Step** Gerri and Jose are modeling fractions. Gerri shades two of four equal parts. Jose models a fraction that is less than Gerfi’s fraction. Which could be the fraction that Jose models?

(A) \(\frac{3}{4}\)

(B) \(\frac{1}{4}\)

(C) \(\frac{2}{4}\)

(D) \(\frac{4}{4}\)

Answer:

It is given that

Gerri and Jose are modeling fractions. Gerri shades two of four equal parts. Jose models a fraction that is less than Gerfi’s fraction

Now,

According to the given information,

The fraction that is modeled by Gerri = \(\frac{2}{4}\)

Now,

We know that,

If the denominators are the same, then the numerators must be compared

Hence, from the above,

We can conclude that

The fraction that Jose modeled is:

Question 16.

**Multi-Step** Mr. Ames baked a slice of banana bread and blueberry bread. The family ate \(\frac{1}{4}\) of the banana bread and \(\frac{3}{4}\) of the blueberry bread. Which bread had more leftover? What fraction of that bread was left over?

(A) blueberry bread, \(\frac{1}{4}\)

(B) blueberry bread, \(\frac{2}{4}\)

(C) banana bread, \(\frac{3}{4}\)

(D) banana bread, \(\frac{2}{4}\)

Answer:

It is given that

Mr. Ames baked a slice of banana bread and blueberry bread. The family ate \(\frac{1}{4}\) of the banana bread and \(\frac{3}{4}\) of the blueberry bread

Now,

The given fractions are:

\(\frac{1}{4}\) and \(\frac{3}{4}\)

Now,

We know that,

if the denominators are the same, then the numerators must be compared

So,

1 < 3

So,

\(\frac{1}{4}\) < \(\frac{3}{4}\)

So,

The type of bread that has more leftovers is: Banana bread

The fraction of the leftover of Banana bread = 1 – \(\frac{1}{4}\)

= \(\frac{4 – 1}{4}\)

= \(\frac{3}{4}\)

Hence, from the above,

We can conclude that

The bread that has more leftovers and the fraction of the leftover is: