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Fractions Flashcards

All 25 cards in this deck

What does it mean to simplify a fraction to its lowest terms?

Divide the numerator and denominator by their highest common factor.
e.g. 1218=23\frac{12}{18}=\frac{2}{3}

What is an equivalent fraction?

A fraction with the same value, made by multiplying or dividing the numerator and denominator by the same number.
e.g. 34=1520\frac{3}{4}=\frac{15}{20}

How do you find a fraction of a quantity?
e.g. 35\frac{3}{5} of 4040

Divide by the denominator, then multiply by the numerator.
40÷5=840\div5=8, 8×3=248\times3=24

In the ratio a:ba:b, what fraction of the total is the first part?
e.g. the ratio 2:32:3

aa+b\frac{a}{a+b}
For 2:32:3 the first part is 25\frac{2}{5} of the total.

True or false? In the ratio 1:41:4, the first quantity is 14\frac{1}{4} of the total.

False. There are 1+4=51+4=5 parts, so the first quantity is 15\frac{1}{5} of the total (and 14\frac{1}{4} of the second quantity).

How do you decide which is bigger, a fraction of one quantity or a fraction of a different quantity?
e.g. 12\frac{1}{2} of 3030 or 13\frac{1}{3} of 6060

Work out each fraction of its own quantity, then compare the two amounts.
1515 and 2020, so 13\frac{1}{3} of 6060 is bigger.

What is an improper fraction?

A fraction whose numerator is greater than or equal to its denominator.
e.g. 73\frac{7}{3}

What are the steps to write a mixed number as an improper fraction?
e.g. 2132\frac{1}{3}

  1. Multiply the whole number by the denominator: 2×3=62\times3=6
  2. Add the numerator: 6+1=76+1=7
  3. Keep the same denominator: 73\frac{7}{3}

What are the steps to write an improper fraction as a mixed number?
e.g. 175\frac{17}{5}

  1. Divide numerator by denominator: 17÷5=317\div5=3 remainder 22
  2. The quotient is the whole number: 33
  3. The remainder is the new numerator: 3253\frac{2}{5}

True or false? An improper fraction is always greater than 1.

False. It is greater than or equal to 1, e.g. 55=1\frac{5}{5}=1.

True or false? When a mixed number is converted to an improper fraction, the denominator stays the same.

True. Only the numerator changes, e.g. 314=1343\frac{1}{4}=\frac{13}{4}.

Which denominator should you use when adding or subtracting fractions with different denominators?
e.g. denominators 55 and 33

The lowest common multiple of the denominators.
For 55 and 33 this is 1515.

What are the steps to add two fractions with different denominators?
e.g. 14+16\frac{1}{4}+\frac{1}{6}

  1. Find a common denominator: 1212
  2. Write equivalent fractions: 312+212\frac{3}{12}+\frac{2}{12}
  3. Add the numerators, keep the denominator: 512\frac{5}{12}

What are the steps to subtract two mixed numbers?
e.g. 312−1163\frac{1}{2}-1\frac{1}{6}

  1. Convert to improper fractions: 72−76\frac{7}{2}-\frac{7}{6}
  2. Use a common denominator: 216−76=146\frac{21}{6}-\frac{7}{6}=\frac{14}{6}
  3. Simplify and write as a mixed number: 2132\frac{1}{3}

True or false? To add two fractions you add the numerators and add the denominators.

False. You only add the numerators, once the fractions share a common denominator.

True or false? Changing fractions into decimals is a reliable way to get an exact answer to a fraction calculation.

False. Fractions such as 23\frac{2}{3} give recurring decimals, so decimals may be rounded; work in fractions to be exact.

How do you deal with adding a negative fraction?
e.g. 15+(−25)\frac{1}{5}+\left(-\frac{2}{5}\right)

Adding a negative fraction is the same as subtracting it.
15−25=−15\frac{1}{5}-\frac{2}{5}=-\frac{1}{5}

How do you multiply two fractions?
e.g. 23×45\frac{2}{3}\times\frac{4}{5}

Multiply the numerators, multiply the denominators, then simplify.
2×43×5=815\frac{2\times4}{3\times5}=\frac{8}{15}

What is the reciprocal of a fraction ab\frac{a}{b}?
e.g. 34\frac{3}{4}

ba\frac{b}{a} — turn the fraction upside down.
The reciprocal of 34\frac{3}{4} is 43\frac{4}{3}.

What is the rule for dividing by a fraction?
e.g. 25÷34\frac{2}{5}\div\frac{3}{4}

Multiply by the reciprocal of the second fraction.
25×43=815\frac{2}{5}\times\frac{4}{3}=\frac{8}{15}

What are the steps to divide with mixed numbers, giving the answer as a mixed number?
e.g. 134÷341\frac{3}{4}\div\frac{3}{4}

  1. Convert to improper fractions: 74÷34\frac{7}{4}\div\frac{3}{4}
  2. Multiply by the reciprocal: 74×43=2812\frac{7}{4}\times\frac{4}{3}=\frac{28}{12}
  3. Simplify and write as a mixed number: 73=213\frac{7}{3}=2\frac{1}{3}

What are the steps to multiply two mixed numbers?
e.g. 213×3342\frac{1}{3}\times3\frac{3}{4}

  1. Convert to improper fractions: 73×154\frac{7}{3}\times\frac{15}{4}
  2. Multiply numerators and denominators: 10512=354\frac{105}{12}=\frac{35}{4}
  3. Write as a mixed number: 8348\frac{3}{4}

True or false? You need a common denominator before you can multiply two fractions.

False. A common denominator is only needed for adding and subtracting; to multiply, just multiply numerators and denominators.

True or false? 14\frac{1}{4} of one quantity is always less than 13\frac{1}{3} of another quantity.

False. The quantities may be different sizes, so you must work out each amount before comparing.

How do you decide which of two fractions of the same quantity gives the larger amount?

e.g. 35\frac{3}{5} of £30 or 23\frac{2}{3} of £30

Compare the fractions using a common denominator; the larger fraction gives the larger amount.

915<1015\frac{9}{15}<\frac{10}{15}, so 23\frac{2}{3} of £30 is more.