Simplifying a Ratio of Decimals Online Quiz

Answer : A

Explanation

Step 1:

Given ratio 3.5:7.7 in fraction form = $\frac{3.5}{7.7}$

Step 2:

Multiply Numerator and Denominator with 10 $\frac{3.5}{7.7} = \frac{\left (3.5 \times 10 \right )}{\left ( 7.7 \times 10 \right )} = \frac{35}{77}$

Step 3:

Divide Numerator and Denominator with HCF of 35 and 77, which is 7

$\frac{35}{77} = \frac{\left (35 \div 7 \right )}{\left ( 77 \div 7 \right )} = \frac{5}{11}$

$\frac{5}{11}$ back in ratio form = 5:11

Step 4:

So, 3.5:7.7 = 5:11 in lowest terms

Q 2 - Simplify the ratio 1.2:1.36 to its lowest terms.

Answer : C

Explanation

Step 1:

Given ratio 1.2:1.36 in fraction form = $\frac{1.2}{1.36}$

Step 2:

Multiply Numerator and Denominator with 100 $\frac{1.2}{1.36} = \frac{\left (1.2 \times 100 \right )}{\left ( 1.36 \times 100 \right )} = \frac{120}{136}$

Step 3:

Divide Numerator and Denominator with HCF of 120 and 136, which is 8

$\frac{120}{136} = \frac{\left (120 \div 8 \right )}{\left ( 136 \div 8 \right )} = \frac{15}{17}$

$\frac{15}{17}$ back in ratio form = 15:17

Step 4:

So, 1.2:1.36 = 15:17 in lowest terms

Q 3 - Simplify the ratio 2.8:5.18 to its lowest terms.

Answer : D

Explanation

Step 1:

Given ratio 2.8:5.18 in fraction form = $\frac{2.8}{5.18}$

Step 2:

Multiply Numerator and Denominator with 100 $\frac{2.8}{5.18} = \frac{\left ( 2.8 \times 100 \right )}{\left ( 5.18 \times 100 \right )} = \frac{280}{518}$

Step 3:

Divide Numerator and Denominator with HCF of 280 and 518, which is 14

$\frac{280}{518} = \frac{\left ( 280 \div 14 \right )}{\left ( 518 \div 14 \right )} = \frac{20}{37}$

$\frac{20}{37}$ back in ratio form = 20:37

Step 4:

So, 2.8:5.18 = 20:37 in lowest terms

Q 4 - Simplify the ratio 5.6:72.8 to its lowest terms.

Answer : B

Explanation

Step 1:

Given ratio 5.6:72.8 in fraction form = $\frac{5.6}{72.8}$

Step 2:

Multiply Numerator and Denominator with 10 $\frac{5.6}{72.8} = \frac{\left ( 5.6 \times 10 \right )}{\left ( 72.8 \times 10 \right )} = \frac{56}{728}$

Step 3:

Divide Numerator and Denominator with HCF of 56 and 728, which is 56

$\frac{56}{728} = \frac{\left ( 56 \div 56 \right )}{\left ( 728 \div 56 \right )} = \frac{1}{13}$

$\frac{1}{13}$ back in ratio form = 1:13

Step 4:

So, 5.6:72.8 = 1:13 in lowest terms

Q 5 - Simplify the ratio 54.6:43.2 to its lowest terms.

Answer : C

Explanation

Step 1:

Given ratio 54.6:43.2 in fraction form = $\frac{54.6}{43.2}$

Step 2:

Multiply Numerator and Denominator with 10 $\frac{54.6}{43.2} = \frac{\left (54.6 \times 10 \right )}{\left ( 43.2 \times 10 \right )} = \frac{546}{432}$

Step 3:

Divide Numerator and Denominator with HCF of 546 and 432, which is 6

$\frac{546}{432} = \frac{\left ( 546 \div 6 \right )}{\left ( 432 \div 6 \right )} = \frac{91}{72}$

$\frac{91}{72}$ back in ratio form = 91:72

Step 4:

So, 54.6:43.2 = 91:72 in lowest terms

Q 6 - Simplify the ratio 1.4:4.9 to its lowest terms.

Answer : A

Explanation

Step 1:

Given ratio 1.4:4.9 in fraction form = $\frac{1.4}{4.9}$

Step 2:

Multiply Numerator and Denominator with 10 $\frac{1.4}{4.9} = \frac{\left ( 1.4 \times 10 \right )}{\left ( 4.9 \times 10 \right )} = \frac{14}{49}$

Step 3:

Divide Numerator and Denominator with HCF of 14 and 49, which is 7

$\frac{14}{49} = \frac{\left ( 14 \div 7 \right )}{\left ( 49 \div 7 \right )} = \frac{2}{7}$

$\frac{2}{7}$ back in ratio form = 2:7

Step 4:

So, 1.4:4.9 = 2:7 in lowest terms

Q 7 - Simplify the ratio 1.8:3.0 to its lowest terms.

Answer : D

Explanation

Step 1:

Given ratio 1.8:3.0 in fraction form = $\frac{1.8}{3.0}$

Step 2:

Multiply Numerator and Denominator with 10 $\frac{1.8}{3.0} = \frac{\left ( 1.8 \times 10 \right )}{\left ( 3.0 \times 10 \right )} = \frac{18}{30}$

Step 3:

Divide Numerator and Denominator with HCF of 18 and 30, which is 6

$\frac{18}{30} = \frac{\left ( 18 \div 6 \right )}{\left ( 30 \div 6 \right )} = \frac{3}{5}$

$\frac{3}{5}$ back in ratio form = 3:5

Step 4:

So, 1.8:3.0 = 3:5 in lowest terms

Q 8 - Simplify the ratio 2.8:9.1 to its lowest terms.

Answer : C

Explanation

Step 1:

Given ratio 2.8:9.1 in fraction form = $\frac{2.8}{9.1}$

Step 2:

Multiply Numerator and Denominator with 10 $\frac{2.8}{9.1} = \frac{\left ( 2.8 \times 10 \right )}{\left ( 9.1 \times 10 \right )} = \frac{28}{91}$

Step 3:

Divide Numerator and Denominator with HCF of 28 and 91, which is 7

$\frac{28}{91} = \frac{\left ( 28 \div 7 \right )}{\left ( 91 \div 7 \right )} = \frac{4}{13}$

$\frac{4}{13}$ back in ratio form = 4:13

Step 4:

So, 2.8:9.1 = 4:13 in lowest terms

Q 9 - Simplify the ratio 3.0:7.8 to its lowest terms.

Answer : B

Explanation

Step 1:

Given ratio 3.0:7.8 in fraction form = $\frac{3.0}{7.8}$

Step 2:

Multiply Numerator and Denominator with 10 $\frac{3.0}{7.8} = \frac{\left ( 3.0 \times 10 \right )}{\left ( 7.8 \times 10 \right )} = \frac{30}{78}$

Step 3:

Divide Numerator and Denominator with HCF of 30 and 78, which is 6

$\frac{30}{78} = \frac{\left ( 30 \div 6 \right )}{\left ( 78 \div 6 \right )} = \frac{5}{13}$

$\frac{5}{13}$ back in ratio form = 5:13

Step 4:

So, 3.0:7.8 = 5:13 in lowest terms

Q 10 - Simplify the ratio 1.2:1.48 to its lowest terms.

Answer : A

Explanation

Step 1:

Given ratio 1.2:1.48 in fraction form = $\frac{1.2}{1.48}$

Step 2:

Multiply Numerator and Denominator with 100 $\frac{1.2}{1.48} = \frac{\left ( 1.2 \times 10 \right )}{\left ( 1.48 \times 10 \right )} = \frac{120}{148}$

Step 3:

Divide Numerator and Denominator with HCF of 120 and 148, which is 4

$\frac{120}{148} = \frac{\left ( 120 \div 4 \right )}{\left ( 148 \div 4 \right )} = \frac{30}{37}$

$\frac{30}{37}$ back in ratio form = 30:37

Step 4:

So, 1.2:1.48 = 30:37 in lowest terms

simplifying_ratio_decimals.htm

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