Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 4 Ratio to finish your assignments.

## Math in Focus Grade 6 Course 1 A Chapter 4 Answer Key Ratio

### Math in Focus Grade 6 Chapter 4 Quick Check Answer Key

**Express each fraction as two equivalent fractions using division.**

Question 1.

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

Answer:

\(\frac{6}{8}\) and \(\frac{9}{12}\)

Explanation:

To find equivalent fractions,

just multiply the numerator and denominator of that reduced fraction (3/4) by any integer number, i.e., multiply by 2, 3, 4 and so on.

\(\frac{3×2}{4×2}\) = \(\frac{6}{8}\)

\(\frac{3×3}{4×3}\) = \(\frac{9}{12}\)

Question 2.

\(\frac{7}{9}\)

Answer:

\(\frac{14}{18}\) and \(\frac{21}{27}\)

Explanation:

To find equivalent fractions,

just multiply the numerator and denominator of that reduced fraction (7/9) by any integer number, i.e., multiply by 2, 3, 10, 30 and so on.

\(\frac{7×2}{9×2}\) = \(\frac{14}{18}\)

\(\frac{7×3}{9×3}\) = \(\frac{21}{27}\)

Question 3.

\(\frac{6}{11}\)

Answer:

\(\frac{12}{22}\) and \(\frac{18}{33}\)

Explanation:

To find equivalent fractions,

just multiply the numerator and denominator of that reduced fraction (6/11) by any integer number, i.e., multiply by 2, 3, 10, 30 and so on.

\(\frac{6×2}{11×2}\) = \(\frac{12}{22}\)

\(\frac{6×3}{11×3}\) = \(\frac{18}{33}\)

Question 4.

\(\frac{16}{56}\)

Answer:

\(\frac{4}{14}\) and \(\frac{2}{7}\)

Explanation:

To find equivalent fractions,

Divide the numerator and denominator to reduce fraction (16/56) by 4 and 2.

\(\frac{16}{56}\) ÷ 4

= \(\frac{4}{14}\) ÷ 2

= \(\frac{2}{7}\)

Question 5.

\(\frac{21}{63}\)

Answer:

\(\frac{1}{3}\) and \(\frac{2}{6}\)

Explanation:

To find equivalent fractions,

Divide the numerator and denominator to reduce fraction \(\frac{21}{63}\) by 21.

\(\frac{21}{63}\) ÷ 1

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

Multiply with integer 2

\(\frac{1×2}{3×2}\)

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

Question 6.

\(\frac{35}{140}\)

Answer:

\(\frac{1}{4}\) and \(\frac{2}{8}\)

Explanation:

To find equivalent fractions,

Divide the numerator and denominator to reduce fraction \(\frac{35}{140}\) by 35.

\(\frac{35}{140}\) ÷ 35

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

Multiply with integer 2

\(\frac{1×2}{4×2}\)

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

**Find the unknown numerator or denominator in each pair of equivalent fractions.**

Question 7.

\(\frac{3}{8}\) = \(\frac{?}{56}\)

Answer: 21

Explanation:

Use cross multiplication to calculate the unknown variable x or fraction.

\(\frac{3}{8}\) = \(\frac{?}{56}\)

\(\frac{3×56}{8}\) = \(\frac{168}{8}\) = 21

Question 8.

\(\frac{7}{9}\) = \(\frac{21}{?}\)

Answer: 27

Explanation:

Use cross multiplication to calculate the unknown variable x or fraction.

\(\frac{7}{9}\) = \(\frac{21}{?}\)

\(\frac{9×21}{7}\) = \(\frac{189}{7}\) = 27

Question 9.

\(\frac{?}{11}\) = \(\frac{30}{55}\)

Answer: 6

Explanation:

Use cross multiplication to calculate the unknown variable x or fraction.

\(\frac{?}{11}\) = \(\frac{30}{55}\)

\(\frac{30×11}{55}\) = \(\frac{330}{55}\) = 6

Question 10.

\(\frac{6}{?}\) = \(\frac{42}{84}\)

Answer: 12

Explanation:

Use cross multiplication to calculate the unknown variable x or fraction.

\(\frac{6}{?}\) = \(\frac{42}{84}\)

\(\frac{6×84}{42}\) = \(\frac{504}{42}\) = 12

**Writing fractions in simplest form**

Question 11.

\(\frac{5}{45}\)

Answer:

\(\frac{1}{9}\)

Explanation:

If the numerator and denominator can be divided by the same number,

which is called a common factor a simple form of fraction.

See if at least one number in the fraction is a prime number.

Question 12.

\(\frac{18}{63}\)

Answer:

\(\frac{2}{7}\)

Explanation:

If the numerator and denominator can be divided by the same number,

which is called a common factor a simple form of fraction.

See if at least one number in the fraction is a prime number.

Question 13.

\(\frac{22}{55}\)

Answer:

\(\frac{2}{5}\)

Explanation:

If the numerator and denominator can be divided by the same number,

which is called a common factor a simple form of fraction.

See if at least one number in the fraction is a prime number.

**Find the unknown measurement.**

Question 14.

cm = 4 m

Answer:

400 cm

Explanation:

1m = 100 cm

4 m = 4 x 100

= 400 cm

Question 15.

9.8 kg = g

Answer:

9800 g

Explanation:

1 kg = 1000 g

9.8 kg = 1000 x 9.8

= 9800 g

Question 16.

6 ft = yd

Answer:

2 yards

Explanation:

1 feet = 0.33 yards

6 feet = 0.333 x 6

= 2 yards

Question 17.

10 L = mL

Answer:

10000 mL

Explanation:

1 L = 1000 mL

10 L = 1000 x 10

= 10000 mL

Question 18.

yd = 72 in.

Answer:

2 yards

Explanation:

1 yd = 36 in

72 in = 72/36 = 2

Question 19.

5 lb = oz

Answer:

80 oz

Explanation:

1 lb = 16 oz

5 lb = 16 x 5 = 80

**Find the values of P and Q.**

Question 20.

Answer:

P = 24 and Q = 6

Explanation:

Each block is of 6 units, as shown below picture

P is of four blocks 6 x 4 = 24 and

Q is 6

Question 21.

Answer:

P = 12 and Q = 16

Explanation:

Each bock is of 4 units

P is 4 x 3 =12 and Q is 4 x 4 = 16