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Core Connections: Course 2

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Core Connections: Course 2 View details

2. Section 3.2

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Exercise 38 Page 144

Practice makes perfect

When adding or subtracting fractions, they should have the same denominator. In this exercise, we have two fractions with different denominators.

\frac{3}{4} + \frac{2}{3}

Since

12

is a multiple of both

4

and

3,

we can first multiply both the numerator and denominator of

\frac{3}{4}

by

3

to create a common denominator.

\frac{3}{4} + \frac{2}{3}

$\frac{a}{b} = \frac{a \cdot 3}{b \cdot 3}$

\frac{3 \cdot 3}{4 \cdot 3} + \frac{2}{3}

Multiply

\frac{9}{1 2} + \frac{2}{3}

Next, we can multiply both the numerator and denominator of

\frac{2}{3}

by

4

to create a common denominator.

\frac{9}{1 2} + \frac{2}{3}

$\frac{a}{b} = \frac{a \cdot 4}{b \cdot 4}$

\frac{9}{1 2} + \frac{2 \cdot 4}{3 \cdot 4}

Multiply

\frac{9}{1 2} + \frac{8}{1 2}

Now that we have a common denominator, we can proceed to simplifying the expression.

\frac{9}{1 2} + \frac{8}{1 2}

Add fractions

\frac{9 + 8}{1 2}

Add terms

\frac{1 7}{1 2}

Write fraction as a mixed number

1 \frac{5}{1 2}

When adding or subtracting fractions, they should have the same denominator. In this exercise, we have two fractions with different denominators.

\frac{7}{8} - \frac{1}{4}

Since

8

is a multiple of

4,

we can multiply both the numerator and denominator of

\frac{1}{4}

by

2

to create a common denominator.

\frac{7}{8} - \frac{1}{4}

$\frac{a}{b} = \frac{a \cdot 2}{b \cdot 2}$

\frac{7}{8} - \frac{1 \cdot 2}{4 \cdot 2}

Multiply

\frac{7}{8} - \frac{2}{8}

Now that we have a common denominator, we can proceed to simplifying the expression.

\frac{7}{8} - \frac{2}{8}

Subtract fractions

\frac{7 - 2}{8}

Subtract term

\frac{5}{8}

When we multiply fractions, we need to remember that the product of two fractions is equal to the product of the numerators divided by the product of the denominators. Let's find the given product!

\frac{3}{5} \cdot \frac{1}{3}

Multiply fractions

\frac{3 \cdot 1}{5 \cdot 3}

Multiply

\frac{3}{1 5}

$\frac{a}{b} = \frac{a / 3}{b / 3}$

\frac{1}{5}

When we multiply fractions, we need to remember that the product of two fractions is equal to the product of the numerators divided by the product of the denominators. Let's find the given product!

\frac{4}{7} \cdot \frac{2}{3}

Multiply fractions

\frac{4 \cdot 2}{7 \cdot 3}

Multiply

\frac{8}{2 1}

Subchapter links

3.2.1 Subtraction of Integers p.143-144

3.2.2 Connecting Addition and Subtraction p.147-148

3.2.3 Multiplication as Repeated Subtraction p.152

3.2.4 Multiplication of Decimals p.158

3.2.5 Addition, Subtraction, Multiplication, and Division of Integers p.161