Solved on Jan 12, 2024

Simplify the following fraction multiplications: $\frac{1}{2} \times \frac{6}{7}$ and $\frac{5}{6} \times \frac{3}{9}$ .

STEP 1

Assumptions
1. We are performing multiplication of two fractions in each part of the problem.
2. To multiply two fractions, we multiply the numerators together and the denominators together.

STEP 2

Let's solve part (a) of the problem. Multiply the numerators of the two fractions.
$\frac{1}{2} \times \frac{6}{7} = \frac{1 \times 6}{2 \times 7}$

STEP 3

Now, multiply the denominators of the two fractions.
$\frac{1 \times 6}{2 \times 7} = \frac{6}{14}$

STEP 4

Simplify the fraction if possible. In this case, both the numerator and the denominator are divisible by 2.
$\frac{6}{14} = \frac{6 \div 2}{14 \div 2}$

STEP 5

Perform the division to simplify the fraction.
$\frac{6 \div 2}{14 \div 2} = \frac{3}{7}$

STEP 6

The solution for part (a) is $\frac{3}{7}$ .

STEP 7

Now, let's solve part (b) of the problem. Multiply the numerators of the two fractions.
$\frac{5}{6} \times \frac{3}{9} = \frac{5 \times 3}{6 \times 9}$

STEP 8

Now, multiply the denominators of the two fractions.
$\frac{5 \times 3}{6 \times 9} = \frac{15}{54}$

STEP 9

Simplify the fraction if possible. In this case, both the numerator and the denominator are divisible by 3.
$\frac{15}{54} = \frac{15 \div 3}{54 \div 3}$

STEP 10

Perform the division to simplify the fraction.
$\frac{15 \div 3}{54 \div 3} = \frac{5}{18}$

STEP 11

The solution for part (b) is $\frac{5}{18}$ .
The solutions are: a. $\frac{3}{7}$ b. $\frac{5}{18}$

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Simplify the following fraction multiplications: $\frac{1}{2} \times \frac{6}{7}$ and $\frac{5}{6} \times \frac{3}{9}$ .

STEP 1

Assumptions
1. We are performing multiplication of two fractions in each part of the problem.
2. To multiply two fractions, we multiply the numerators together and the denominators together.

STEP 2

Let's solve part (a) of the problem. Multiply the numerators of the two fractions.
$\frac{1}{2} \times \frac{6}{7} = \frac{1 \times 6}{2 \times 7}$

STEP 3

Now, multiply the denominators of the two fractions.
$\frac{1 \times 6}{2 \times 7} = \frac{6}{14}$

STEP 4

Simplify the fraction if possible. In this case, both the numerator and the denominator are divisible by 2.
$\frac{6}{14} = \frac{6 \div 2}{14 \div 2}$

STEP 5

Perform the division to simplify the fraction.
$\frac{6 \div 2}{14 \div 2} = \frac{3}{7}$

STEP 6

The solution for part (a) is $\frac{3}{7}$ .

STEP 7

Now, let's solve part (b) of the problem. Multiply the numerators of the two fractions.
$\frac{5}{6} \times \frac{3}{9} = \frac{5 \times 3}{6 \times 9}$

STEP 8

Now, multiply the denominators of the two fractions.
$\frac{5 \times 3}{6 \times 9} = \frac{15}{54}$

STEP 9

Simplify the fraction if possible. In this case, both the numerator and the denominator are divisible by 3.
$\frac{15}{54} = \frac{15 \div 3}{54 \div 3}$

STEP 10

Perform the division to simplify the fraction.
$\frac{15 \div 3}{54 \div 3} = \frac{5}{18}$

STEP 11

The solution for part (b) is $\frac{5}{18}$ .
The solutions are: a. $\frac{3}{7}$ b. $\frac{5}{18}$

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Simplify the following fraction multiplications: 12×67\frac{1}{2} \times \frac{6}{7}21​×76​ and 56×39\frac{5}{6} \times \frac{3}{9}65​×93​.

STEP 1

Assumptions1. We are performing multiplication of two fractions in each part of the problem.2. To multiply two fractions, we multiply the numerators together and the denominators together.

STEP 2

Let's solve part (a) of the problem. Multiply the numerators of the two fractions.12×67=1×62×7\frac{1}{2} \times \frac{6}{7} = \frac{1 \times 6}{2 \times 7}21​×76​=2×71×6​

STEP 3

Now, multiply the denominators of the two fractions.1×62×7=614\frac{1 \times 6}{2 \times 7} = \frac{6}{14}2×71×6​=146​

STEP 4

Simplify the fraction if possible. In this case, both the numerator and the denominator are divisible by 2.614=6÷214÷2\frac{6}{14} = \frac{6 \div 2}{14 \div 2}146​=14÷26÷2​

STEP 5

Perform the division to simplify the fraction.6÷214÷2=37\frac{6 \div 2}{14 \div 2} = \frac{3}{7}14÷26÷2​=73​

STEP 6

The solution for part (a) is 37\frac{3}{7}73​.

STEP 7

Now, let's solve part (b) of the problem. Multiply the numerators of the two fractions.56×39=5×36×9\frac{5}{6} \times \frac{3}{9} = \frac{5 \times 3}{6 \times 9}65​×93​=6×95×3​

STEP 8

Now, multiply the denominators of the two fractions.5×36×9=1554\frac{5 \times 3}{6 \times 9} = \frac{15}{54}6×95×3​=5415​

STEP 9

Simplify the fraction if possible. In this case, both the numerator and the denominator are divisible by 3.1554=15÷354÷3\frac{15}{54} = \frac{15 \div 3}{54 \div 3}5415​=54÷315÷3​

STEP 10

Perform the division to simplify the fraction.15÷354÷3=518\frac{15 \div 3}{54 \div 3} = \frac{5}{18}54÷315÷3​=185​

STEP 11

The solution for part (b) is 518\frac{5}{18}185​.The solutions are: a. 37\frac{3}{7}73​ b. 518\frac{5}{18}185​

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Simplify the following fraction multiplications: $\frac{1}{2} \times \frac{6}{7}$ and $\frac{5}{6} \times \frac{3}{9}$ .

Assumptions
1. We are performing multiplication of two fractions in each part of the problem.
2. To multiply two fractions, we multiply the numerators together and the denominators together.

Let's solve part (a) of the problem. Multiply the numerators of the two fractions.
$\frac{1}{2} \times \frac{6}{7} = \frac{1 \times 6}{2 \times 7}$

Now, multiply the denominators of the two fractions.
$\frac{1 \times 6}{2 \times 7} = \frac{6}{14}$

Simplify the fraction if possible. In this case, both the numerator and the denominator are divisible by 2.
$\frac{6}{14} = \frac{6 \div 2}{14 \div 2}$

Perform the division to simplify the fraction.
$\frac{6 \div 2}{14 \div 2} = \frac{3}{7}$

The solution for part (a) is $\frac{3}{7}$ .

Now, let's solve part (b) of the problem. Multiply the numerators of the two fractions.
$\frac{5}{6} \times \frac{3}{9} = \frac{5 \times 3}{6 \times 9}$

Now, multiply the denominators of the two fractions.
$\frac{5 \times 3}{6 \times 9} = \frac{15}{54}$

Simplify the fraction if possible. In this case, both the numerator and the denominator are divisible by 3.
$\frac{15}{54} = \frac{15 \div 3}{54 \div 3}$

Perform the division to simplify the fraction.
$\frac{15 \div 3}{54 \div 3} = \frac{5}{18}$

The solution for part (b) is $\frac{5}{18}$ .
The solutions are: a. $\frac{3}{7}$ b. $\frac{5}{18}$