Fractions Flashcards

All 36 cards in this deck

What does the denominator of a fraction tell you?

The number of equal parts the whole is divided into.

e.g. in $\frac{3}{10}$ the whole is split into 10 equal parts.

What does the numerator of a fraction tell you?

How many of the equal parts are being counted.

e.g. in $\frac{3}{10}$, 3 of the parts are counted.

How do you write the fraction of a shape or set that is shaded?

e.g. 3 of 10 identical squares are shaded

$\frac{\text{number of shaded parts}}{\text{total number of equal parts}}$, so $\frac{3}{10}$.

What are the steps to write fractions in order of size, smallest first?

e.g. $\frac{1}{2}$, $\frac{1}{3}$, $\frac{5}{6}$

1. Write them with a common denominator: $\frac{3}{6}$, $\frac{2}{6}$, $\frac{5}{6}$
2. Compare the numerators: 2, 3, 5
3. List the original fractions in that order: $\frac{1}{3}$, $\frac{1}{2}$, $\frac{5}{6}$

What are the steps to decide which of two fractions is closer to $\frac{1}{2}$?

e.g. $\frac{3}{5}$ and $\frac{5}{8}$

1. Common denominator with $\frac{1}{2}$: $\frac{20}{40}$, $\frac{24}{40}$, $\frac{25}{40}$
2. Find each distance from $\frac{1}{2}$: $\frac{4}{40}$ and $\frac{5}{40}$
3. Smaller distance is closer: $\frac{3}{5}$

In a calculation like "$\frac{1}{3}$ of 24", what operation does the word "of" mean?

Multiply: $\frac{1}{3}\times 24=8$.

What are the steps to find a fraction of a quantity?

e.g. $\frac{2}{5}$ of 40

1. Divide by the denominator: $40\div 5=8$
2. Multiply by the numerator: $8\times 2=16$

True or false? To find $\frac{3}{4}$ of an amount you divide by 3 and multiply by 4.

False.

You divide by the denominator (4) and multiply by the numerator (3).

What are the steps to find the whole when you are given a fraction of it?

e.g. $\frac{2}{3}$ of a number is 48

1. Divide by the numerator to get one part: $48\div 2=24$
2. Multiply by the denominator: $24\times 3=72$

The number is 72.

What are the steps to find a fraction of what is left over?

e.g. a 52 litre tank is $\frac{1}{4}$ full — how many more litres fill it?

1. Subtract from 1 to get the fraction left: $1-\frac{1}{4}=\frac{3}{4}$
2. Find that fraction of the amount: $\frac{3}{4}\times 52=39$ litres

What is an equivalent fraction?

A fraction of the same value, made by multiplying or dividing the numerator and denominator by the same number.

e.g. $\frac{3}{4}=\frac{6}{8}$

What does it mean for a fraction to be in its simplest form?

The numerator and denominator have no common factor other than 1.

What are the steps to write a fraction in its simplest form?

e.g. $\frac{12}{18}$

1. Find the highest common factor of the numerator and denominator: 6
2. Divide both by it: $\frac{12\div 6}{18\div 6}=\frac{2}{3}$

What are the steps to write one quantity as a fraction of another in its simplest form?

e.g. 60 m as a fraction of 1000 m

1. Write it as $\frac{\text{part}}{\text{whole}}$: $\frac{60}{1000}$
2. Divide both by their highest common factor (20): $\frac{3}{50}$

True or false? Multiplying the numerator and the denominator by the same number changes the value of a fraction.

False.

It gives an equivalent fraction of the same value, e.g. $\frac{2}{5}=\frac{8}{20}$.

How do you find a common denominator for two fractions?

e.g. $\frac{2}{5}$ and $\frac{1}{4}$

Use a common multiple of the two denominators and make equivalent fractions.

20 works: $\frac{8}{20}$ and $\frac{5}{20}$.

What is an improper fraction?

A fraction whose numerator is greater than or equal to its denominator, so its value is 1 or more.

e.g. $\frac{7}{3}$

What is a mixed number?

A whole number written together with a proper fraction.

e.g. $2\frac{1}{3}$

What are the steps to change a mixed number into an improper fraction?

e.g. $3\frac{2}{5}$

1. Multiply the whole number by the denominator: $3\times 5=15$
2. Add the numerator: $15+2=17$
3. Keep the same denominator: $\frac{17}{5}$

What are the steps to change an improper fraction into a mixed number?

e.g. $\frac{17}{5}$

1. Divide numerator by denominator: $17\div 5=3$ remainder 2
2. Whole number is 3, remainder goes over the denominator: $3\frac{2}{5}$

True or false? To change $3\frac{2}{5}$ into an improper fraction you multiply 3 by 2.

False.

You multiply the whole number by the denominator, then add the numerator: $\frac{17}{5}$.

What is the first step when multiplying or dividing mixed numbers?

Convert each mixed number into an improper fraction.

e.g. $2\frac{1}{3}=\frac{7}{3}$

How do you add fractions that already have the same denominator?

e.g. $\frac{3}{7}+\frac{2}{7}$

Add the numerators and keep the denominator the same: $\frac{5}{7}$.

What are the steps to add fractions with different denominators?

e.g. $\frac{2}{5}+\frac{1}{4}$

1. Write both with a common denominator: $\frac{8}{20}$ and $\frac{5}{20}$
2. Add the numerators, keeping the denominator: $\frac{13}{20}$

True or false? $\frac{1}{2}+\frac{1}{3}=\frac{2}{5}$ because you add the numerators and add the denominators.

False.

You must use a common denominator: $\frac{3}{6}+\frac{2}{6}=\frac{5}{6}$.

What fraction must be added to $\frac{2}{7}$ to make 1?

$\frac{5}{7}$, because 1 whole is $\frac{7}{7}$.

What are the steps to subtract mixed numbers when the fraction parts need borrowing?

e.g. $3\frac{1}{5}-1\frac{2}{3}$

1. Convert both to improper fractions: $\frac{16}{5}-\frac{5}{3}$
2. Use a common denominator: $\frac{48}{15}-\frac{25}{15}$
3. Subtract the numerators and convert back: $\frac{23}{15}=1\frac{8}{15}$

What are the steps to add mixed numbers without converting to improper fractions?

e.g. $2\frac{1}{4}+1\frac{1}{2}$

1. Add the whole numbers: $2+1=3$
2. Add the fractions using a common denominator: $\frac{1}{4}+\frac{2}{4}=\frac{3}{4}$
3. Combine: $3\frac{3}{4}$

What are the steps to multiply two fractions?

e.g. $\frac{5}{8}\times\frac{3}{4}$

1. Multiply the numerators: $5\times 3=15$
2. Multiply the denominators: $8\times 4=32$
3. Simplify if possible: $\frac{15}{32}$

How do you multiply a fraction by an integer?

e.g. $\frac{2}{7}\times 3$

Multiply the numerator by the integer and keep the denominator: $\frac{6}{7}$.

What can you do before multiplying fractions to make the numbers easier?

Cancel any common factor between a numerator and a denominator.

e.g. $\frac{2}{3}\times\frac{3}{4}$: cancel the 3s to get $\frac{2}{4}=\frac{1}{2}$.

What are the steps to divide by a fraction?

e.g. $3\div\frac{5}{6}$

1. Turn the dividing fraction upside down: $\frac{5}{6}\rightarrow\frac{6}{5}$
2. Multiply instead of dividing: $3\times\frac{6}{5}=\frac{18}{5}$
3. Write as a mixed number if asked: $3\frac{3}{5}$

True or false? Dividing a number by $\frac{1}{2}$ is the same as dividing it by 2.

False.

Dividing by $\frac{1}{2}$ means multiplying by 2, e.g. $48\div\frac{1}{2}=96$.

What are the steps to multiply two mixed numbers?

e.g. $2\frac{1}{3}\times 3\frac{3}{4}$

1. Convert to improper fractions: $\frac{7}{3}\times\frac{15}{4}$
2. Multiply numerators and denominators: $\frac{105}{12}=\frac{35}{4}$
3. Convert back to a mixed number: $8\frac{3}{4}$

What are the steps to subtract fractions with different denominators?

e.g. $\frac{5}{6}-\frac{1}{4}$

1. Write both with a common denominator: $\frac{10}{12}-\frac{3}{12}$
2. Subtract the numerators only: $\frac{7}{12}$
3. Simplify if possible: $\frac{7}{12}$

What are the steps to subtract mixed numbers when the first fraction part is too small to subtract from?

e.g. $3\frac{1}{5}-1\frac{2}{3}$

1. Use a common denominator: $3\frac{3}{15}-1\frac{10}{15}$
2. Borrow 1 from the whole as $\frac{15}{15}$: $3\frac{3}{15}=2\frac{18}{15}$
3. Subtract wholes then fractions: $1\frac{8}{15}$