MathMaster Blog

To multiply rational numbers, stick to the rules of multiplying positive and negative numbers:

f the factors have the same sign, the product is positive.

If the factors have different signs, the product is negative.

Multiplying decimals

• Step 1: Multiply as you would with whole numbers.
• Step 2: Count the total number of decimal places in both factors.
• Step 3: Move the decimal point in the product one place to the left for each decimal place you counted.

Example:

Find −1.6 2.4.

Solution:

Step1:

Multiply as you would with whole numbers

Step2:

Move the decimal point in the product one place to the left for each decimal place you counted

As the decimals have different signs, the product is negative.

Answer: – 3.84

Multiplying fractions

• Step 1: Rewrite any mixed numbers as improper fractions.
• Step 2: Multiply the numerators, then multiply the denominators.
• Step 3: Simplify, if needed.

Example:

Find: $1\frac{3}{8} \times (-\frac{4}{9})$

Solution:

Step1:

Rewrite the mixed number as an improper fraction

$1\frac{3}{8} = \frac{11}{8}$

Step2:

Multiply the numerators, and then multiply the denominators

$\frac{11}{8} \times \frac{4}{9} = \frac{11 \cdot 4}{8 \cdot 9} = \frac{44}{72} = \frac{11}{18}$

Answer: $\frac{11}{18}$

Dividing rational numbers

When dividing rational numbers, follow the rules of dividing positive and negative numbers:

• If the dividend and divisor have the same sign, the quotient is positive.
• If the dividend and divisor have different signs, the quotient is negative.

Dividing decimals

• Step 1: Move the decimal point rightwards to make the divisor a whole number. Move the decimal point the same number of places to rightwards in the dividend.
• Step 2: Put the decimal point in the quotient above the decimal point in the dividend.
• Step 3: Divide until there is no remainder, or until the quotient begins to repeat in a pattern. If it is necessary, add zeros.

Example:

Find –1.83÷(–0.6).

Solution:

Step1:

For now, ignore the signs. To make 0.6 a whole number, move the decimal point one place to the right.

1.83 ÷ 0.6 = 18.3 ÷ 6

Step2:

Rewrite in a long division format. Divide until there is no remainder. You will need to add a zero.

Since the dividend and divisor have the same sign, the quotient is positive.

Answer: 3.05

Dividing fractions

• Step 1: Rewrite any mixed numbers as improper fractions.
• Step 2: Multiply the dividend by the reciprocal of the divisor.
• Step 3: Simplify.

Example:

Find: $2\frac{2}{3} \div 1\frac{1}{4}$

Solution:

Step1:

Ignore the signs of the dividend and divisor for now to make it easier to divide.

Step2:

Rewrite the mixed numbers as improper fractions

$\frac{8}{3} \div \frac{5}{4}$

Step3:

Multiply the dividend by the reciprocal of the divisor

$\frac{8}{3} \times \frac{4}{5} = \frac{32}{15}$

Step3:

Write an improper fraction as a mixed number

$\frac{32}{15} = 2\frac{2}{15}$

Since the dividend and divisor have different signs, the quotient is negative.

<>Answer: $-2\frac{2}{15}$