Equal parts and fraction size
Name fractions of one whole and compare unit or like fractions with the same reference whole.
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Decide what the whole is
Take one sheet of paper. Fold it into four equal parts. One part is one quarter of the sheet, written 1/4.
The bottom number, the denominator, tells how many equal parts make the whole. The top number, the numerator, tells how many of those parts you mean. Three of the four equal parts are 3/4 of the sheet.
Two unequal pieces do not each make one half. The pieces must be equal in amount, not just two in number.
Three quarters: three of four equal parts of this one whole strip. Hatching marks the selected parts.
Compare one part of equal wholes
Fold two equal-sized sheets, one into two equal parts and one into four equal parts. A half sheet is larger than a quarter sheet. With the same whole, more equal parts make each part smaller.
So 1/2 > 1/4. For unit fractions, the numerator is one. Among 1/3, 1/6 and 1/12, the smallest piece is 1/12.
This comparison uses the same whole. Half a tiny biscuit need not be bigger than a quarter of a very large cake.
Compare parts of the same size
When the denominators match, the pieces have the same size. Five eighths uses five eighth-pieces; three eighths uses only three. Therefore 5/8 > 3/8.
Check your understanding 1 Which pieces are bigger?
Both comparisons use equal-sized wholes. Compare one part in the first question and several parts of the same size in the second.
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One third is greater than one sixth: 1/3 > 1/6. Two eighths is less than five eighths: 2/8 < 5/8. First check whether you are comparing single pieces or counting pieces of the same size.
Check your understanding 2 Two different comparison jobs
Put 1/5, 1/2 and 1/8 in order from smallest to largest, using equal wholes. Then put 3/8, 1/8 and 7/8 in order. Explain the difference between your methods.
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For unit fractions: 1/8,1/5,1/2; more equal parts make one part smaller. For like fractions: 1/8,3/8,7/8; each piece is an eighth, so count how many pieces are selected.
Name the fraction yourself
Split a strip into six equal parts and mark five. Say what both numbers in your fraction mean. Draw another strip of the same size with just one of its six parts marked. Compare the two marked amounts.
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The fractions are 5/6 and 1/6. Both use sixths of the same whole. Five sixths is greater than one sixth because it contains more pieces of the same size.
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