Fractions & Decimals

Fractions and decimals both represent quantities that may be less than, equal to, or greater than one whole. A fraction uses a numerator and denominator. The numerator tells how many parts are being considered, and the denominator tells how many equal parts make one whole. In the fraction 3/4, the numerator is 3 and the denominator is 4.nnEquivalent fractions name the same amount. For example, 1/2, 2/4, and 4/8 are equivalent. You can create an equivalent fraction by multiplying or dividing the numerator and denominator by the same nonzero number.nnTo compare fractions with the same denominator, compare their numerators. For example, 5/8 is greater than 3/8. When denominators are different, use a common denominator, a visual model, or convert the fractions to decimals.nnTo add or subtract fractions, the denominators must be the same. For example, 2/5 + 1/5 = 3/5. For 1/2 + 1/4, rename 1/2 as 2/4. Then 2/4 + 1/4 = 3/4. Add or subtract the numerators and keep the common denominator.nnTo multiply fractions, multiply the numerators and then multiply the denominators. For example, 2/3 x 3/5 = 6/15, which simplifies to 2/5. To divide by a fraction, multiply by its reciprocal. For example, 3/4 divided by 1/2 becomes 3/4 x 2/1 = 6/4, or 1 1/2.nnDecimals use place value to represent parts of a whole. In 0.47, the 4 is in the tenths place and the 7 is in the hundredths place. Therefore, 0.47 means 47/100.nnTo add or subtract decimals, line up the decimal points so digits with the same place value are aligned. For example, 3.75 + 1.20 = 4.95. Zeros may be added as placeholders without changing the value.nnTo multiply decimals, multiply as though the numbers were whole numbers. Then count the total number of decimal places in both factors and place the decimal point in the product. To divide decimals, make the divisor a whole number by moving its decimal point, and move the decimal point in the dividend the same number of places.nnCommon misconceptions and corrections: Students may add denominators when adding fractions, compare fractions by looking only at the denominators, or misalign decimal place values. Use fraction models, number lines, and place-value charts to show that every part must be equal and that digits must be compared according to their place values.