Grade4 fractions, mixed numbers and decimal notation
The Fractions and Decimals domain tests equivalent fractions, comparing and ordering fractions, adding and subtracting fractions and mixed numbers with like denominators, decimal notation to hundredths, and the relationship between fractions and decimals. Successful answers depend on understanding the same whole and the same-size parts.
Fraction foundations
- Equivalent fractions are made by multiplying or dividing the numerator and denominator by the same nonzero number: 3/4 = 9/12.
- With like denominators, the fraction with the greater numerator is greater. With like numerators, the fraction with the smaller denominator is greater because the parts are larger.
- A mixed number combines a whole number and a fraction. Convert it to an improper fraction by multiplying the whole number by the denominator, adding the numerator, and keeping the denominator.
- Add or subtract fractions with like denominators by operating on the numerators and keeping the denominator. Regroup a whole number when subtracting a larger fraction from a smaller one.
Decimal foundations
- Tenths are written with one decimal place: 1/10 = 0.1. Hundredths use two places: 1/100 = 0.01.
- 0.7 = 7/10 = 70/100, and 0.70 = 0.7. Annexing zeros to the right of a decimal does not change its value.
- Compare decimals place by place from left to right. Write both numbers with the same number of decimal places before deciding.
- Plot decimals on a number line by dividing the space between whole numbers into tenths or hundredths.
Worked example
Add 2 3/8 + 1 7/8. Add the whole numbers: 2 + 1 = 3. Add the fractions: 3/8 + 7/8 = 10/8. Since 10/8 = 1 2/8, the total is 3 + 1 2/8 = 4 2/8 = 4 1/4.
Traps that cost marks
- Adding denominators, such as writing 3/8 + 7/8 = 10/16.
- Comparing 0.4 and 0.15 and choosing 0.15 because 15 > 4; 0.4 = 0.40, so 0.4 is greater.
- Writing 3/100 as 0.3 instead of 0.03.
- Forgetting to regroup when a fraction sum is greater than 1 or when subtracting a larger fraction from a smaller one.
- Treating the numerator and denominator of a mixed number as separate whole numbers.