Adding and Subtracting Fractions and Mixed Numbers

Questions and Answers

What is the result of adding the fractions $\frac{2}{5}$ and $\frac{1}{3}$?

$\frac{3}{8}$

$\frac{23}{30}$

$\frac{17}{15}$

$\frac{11}{15}$ (correct)

What is the result of subtracting $5\frac{1}{4}$ from $7\frac{2}{3}$?

$2\frac{1}{12}$

$2\frac{5}{12}$ (correct)

$1\frac{5}{12}$

$3\frac{1}{12}$

What is the simplest form of the fraction resulting from $\frac{3}{8}$ - $\frac{1}{4}$?

$\frac{1}{8}$ (correct)

$\frac{3}{8}$

$\frac{1}{2}$

$\frac{1}{4}$

When $\frac{5}{6}$ is added to $\frac{2}{9}$, what is the resulting improper fraction?

$\frac{61}{54}$ Signup and view all the answers

What is the sum of $2\frac{2}{5}$ and $3\frac{3}{10}$ as a mixed number?

$6\frac{1}{2}$ Signup and view all the answers

What is the most efficient strategy for determining the sum of two fractions with different denominators?

Find a common denominator and then add the numerators. Signup and view all the answers

When given the problem of subtracting $rac{3}{4}$ from $rac{5}{6}$, which step is essential before performing the subtraction?

Identify a common denominator for both fractions. Signup and view all the answers

Which problem-solving tool would be most beneficial when working with a complex fraction addition problem?

Drawing a visual model or fraction circles. Signup and view all the answers

What common mistake might occur when adding two fractions that do not share a common denominator?

Adding the numerators without adjusting the denominators. Signup and view all the answers

In a problem involving the addition of the fractions $rac{3}{5}$ and $rac{1}{2}$, what is the first action needed?

Calculate the least common multiple of the denominators. Signup and view all the answers

Study Notes

Adding Fractions

To add fractions, find a common denominator, which allows for summation of the numerators.
For 25\frac{2}{5}52 and 13\frac{1}{3}31, the common denominator is 15.
Convert fractions: 25=615\frac{2}{5} = \frac{6}{15}52=156 and 13=515\frac{1}{3} = \frac{5}{15}31=155.
Add them: 615+515=1115\frac{6}{15} + \frac{5}{15} = \frac{11}{15}156+155=1511.

Subtracting Mixed Numbers

When subtracting mixed numbers, first convert them to improper fractions.
5145\frac{1}{4}541 converts to 214\frac{21}{4}421 and 7237\frac{2}{3}732 to 233\frac{23}{3}323.
Find a common denominator, which is 12 in this case.
Convert: 214=6312\frac{21}{4} = \frac{63}{12}421=1263 and 233=9212\frac{23}{3} = \frac{92}{12}323=1292.
Subtract: 9212−6312=2912\frac{92}{12} - \frac{63}{12} = \frac{29}{12}1292−1263=1229, or 25122\frac{5}{12}2125 as a mixed number.

Simplifying Fractions

To simplify the result of 38−14\frac{3}{8} - \frac{1}{4}83−41, first convert 14\frac{1}{4}41 to 28\frac{2}{8}82.
Perform the subtraction: 38−28=18\frac{3}{8} - \frac{2}{8} = \frac{1}{8}83−82=81.
18\frac{1}{8}81 is already in simplest form.

Adding Improper Fractions

When adding fractions like 56\frac{5}{6}65 and 29\frac{2}{9}92, a common denominator is needed, which is 18 here.
Convert fractions: 56=1518\frac{5}{6} = \frac{15}{18}65=1815 and 29=418\frac{2}{9} = \frac{4}{18}92=184.
Add them: 1518+418=1918\frac{15}{18} + \frac{4}{18} = \frac{19}{18}1815+184=1819, which is an improper fraction.

Sum of Mixed Numbers

For adding mixed numbers 2252\frac{2}{5}252 and 33103\frac{3}{10}3103, convert them to improper fractions first.
225=1252\frac{2}{5} = \frac{12}{5}252=512 and 3310=33103\frac{3}{10} = \frac{33}{10}3103=1033.
A common denominator of 10 allows conversion: 125=2410\frac{12}{5} = \frac{24}{10}512=1024.
Add: 2410+3310=5710\frac{24}{10} + \frac{33}{10} = \frac{57}{10}1024+1033=1057.
Convert back to mixed number: 5710=5710\frac{57}{10} = 5\frac{7}{10}1057=5107.

Understanding Simple Fractions and Mixed Numbers

Simple fractions consist of a numerator and a denominator, representing a part of a whole.
Mixed numbers combine a whole number with a fractional part, e.g., 2 1/2 includes the whole number 2 and the fraction 1/2.