Fractions Decimals and Rational Numbers

Learn adding fractions, dividing fractions, multiplying fractions, fractions and decimal notation.

Lesson 3 of 34 parts Practice Flashcards

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Adding Fractions

Objective: Explain adding fractions, apply the stated method, and check its conditions.

Fractions can be added by expressing them with a common nonzero denominator and adding numerators. The denominator specifies the size of each piece and remains unchanged when like-sized pieces are counted. Simplify the resulting fraction by common factors. Do not add denominators when adding fractions.

Formulas

$a/d+b/d=(a+b)/d, d≠0$

Worked examples

Try itFind 6/7+7/7 in simplest form.Show answer

Step 1: The denominators already match. Step 2: Add numerators: (6+7)/7. Step 3: Reduce to 13/7.

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Adding Fractions

Objective: Explain adding fractions, apply the stated method, and check its conditions.

Formulas

$a/d+b/d=(a+b)/d, d≠0$

Worked examples

Try itFind 6/7+7/7 in simplest form.Show answer

Step 1: The denominators already match. Step 2: Add numerators: (6+7)/7. Step 3: Reduce to 13/7.

Dividing Fractions

Objective: Explain dividing fractions, apply the stated method, and check its conditions.

To divide by a nonzero fraction c/d, multiply by its reciprocal d/c. Both original denominators and the divisor must be nonzero. Division can ask how many groups of the divisor size fit into the dividend. Flip the divisor, not the dividend.

Formulas

$(a/b)÷(c/d)=(a/b)(d/c)$

Worked examples

Try itEvaluate (6/7)÷(1/7).Show answer

Step 1: Multiply by the reciprocal of the divisor. Step 2: Compute (6/7)·7. Step 3: The result is 6.

Multiplying Fractions

Objective: Explain multiplying fractions, apply the stated method, and check its conditions.

Multiply numerators and multiply denominators, with nonzero denominators. Common factors may be canceled before or after multiplication. A fraction product can represent taking a fraction of another quantity; it need not be larger than either factor. Multiplying by a number between zero and one reduces a positive quantity.

Formulas

$(a/b)(c/d)=ac/(bd)$

Worked examples

Try itFind (6/7)·(1/7) in simplest form.Show answer

Step 1: Multiply numerators and multiply denominators. Step 2: The product is 6/(49). Step 3: Reduce to 6/49.

Fractions and Decimal Notation

Objective: Explain fractions and decimal notation, apply the stated method, and check its conditions.

A rational number can be written as a fraction of integers with nonzero denominator. Fractions with powers of ten as denominators translate directly into place-value decimals. Every rational number has a terminating or repeating decimal expansion. Not every rational decimal terminates; some repeat.

Formulas

$c/100 = c hundredths$

Worked examples

Try itWrite 7/100 as a decimal.Show answer

Step 1: The denominator is 100. Step 2: Move the decimal point in the numerator two places left. Step 3: The decimal is 0.07.

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