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McGraw-Hill Math Grade 7 Answer Key Lesson 13.2 Proportions and Cross-Multiplying
Exercises
Cross-Multiply
Round to the hundredths place.
Question 1.
\(\frac{x}{5}\) = \(\frac{30}{15}\)
Answer:
Given equation is \(\frac{x}{5}\) = \(\frac{30}{15}\)
To find the x value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
15x = 30 × 5
15x = 150
Divide both sides of the equation by 15.
\(\frac{15x}{15}\) = \(\frac{150}{15}\)
x = 10
Question 2.
\(\frac{z}{3}\) = \(\frac{24}{6}\)
Answer:
Given equation is \(\frac{z}{3}\) = \(\frac{24}{6}\)
To find the z value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
6z = 24 × 3
6z = 72
Divide both sides of the equation by 6.
\(\frac{6z}{6}\) = \(\frac{72}{6}\)
z = 12
Question 3.
\(\frac{14}{z}\) = \(\frac{100}{50}\)
Answer:
Given equation is \(\frac{14}{z}\) = \(\frac{100}{50}\)
To find the z value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
14 × 50 = 100 × z
700 = 100z
Divide both sides of the equation by 100.
\(\frac{700}{100}\) = \(\frac{100z}{100}\)
7 = z
Question 4.
\(\frac{56}{4}\) = \(\frac{y}{20}\)
Answer:
Given equation is \(\frac{56}{4}\) = \(\frac{y}{20}\)
To find the y value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
56 × 20 = y × 4
1120 = 4y
Divide both sides of the equation by 4.
\(\frac{1120}{4}\) = \(\frac{4y}{4}\)
280 = y
Question 5.
\(\frac{45}{9}\) = \(\frac{w}{3}\)
Answer:
Given equation is\(\frac{45}{9}\) = \(\frac{w}{3}\)
To find the w value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
45 × 3 = w × 9
135 = 9w
Divide both sides of the equation by 9.
\(\frac{135}{9}\) = \(\frac{9w}{9}\)
15 = w
Question 6.
\(\frac{14}{x}\) = \(\frac{70}{10}\)
Answer:
Given equation is \(\frac{14}{x}\) = \(\frac{70}{10}\)
To find the x value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
14 ×10 = 70 × x
140 = 70x
Divide both sides of the equation by 70.
\(\frac{140}{70}\) = \(\frac{70x}{70}\)
2 = x
Question 7.
\(\frac{33}{r}\) = \(\frac{11}{3}\)
Answer:
Given equation is \(\frac{33}{r}\) = \(\frac{11}{3}\)
To find the r value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
33 × 3= 11 × r
99 = 11r
Divide both sides of the equation by 11.
\(\frac{99}{11}\) = \(\frac{11r}{11}\)
9 = r
Question 8.
\(\frac{72}{9}\) = \(\frac{24}{z}\)
Answer:
Given equation is \(\frac{72}{9}\) = \(\frac{24}{z}\)
To find the z value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
72 × z = 24 × 9
72z = 216
Divide both sides of the equation by 72.
\(\frac{72z}{72}\) = \(\frac{216}{72}\)
z = 3
Question 9.
\(\frac{3}{2}\) = \(\frac{x}{5}\)
Answer:
Given equation is \(\frac{3}{2}\) = \(\frac{x}{5}\)
To find the x value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
3 × 5 = x × 2
15 = 2x
Divide both sides of the equation by 2.
\(\frac{15}{2}\) = \(\frac{2x}{2}\)
7.5 = x
Question 10.
\(\frac{700}{50}\) = \(\frac{35}{w}\)
Answer:
Given equation is \(\frac{700}{50}\) = \(\frac{35}{w}\)
To find the w value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
700 × w = 35 × 50
700w = 1750
Divide both sides of the equation by 700.
\(\frac{700w}{700}\) = \(\frac{1750}{700}\)
w = 2.5
Question 11.
\(\frac{36}{4}\) = \(\frac{x}{6}\)
Answer:
Given equation is \(\frac{36}{4}\) = \(\frac{x}{6}\)
To find the x value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
36 × 6 = x × 4
216 = 4x
Divide both sides of the equation by 4.
\(\frac{216}{4}\) = \(\frac{4x}{4}\)
54 = x
Question 12.
\(\frac{84}{12}\) = \(\frac{q}{4}\)
Answer:
Given equation is \(\frac{84}{12}\) = \(\frac{q}{4}\)
To find the q value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
84 × 4 = q × 12
336 = 12q
Divide both sides of the equation by 12.
\(\frac{336}{12}\) = \(\frac{12q}{12}\)
28 = q