  ### Home > CC1 > Chapter 4 > Lesson 4.1.3 > Problem4-43

4-43.

Find each sum or difference without a calculator. 1. $\frac { 7 } { 10 } + \frac { 2 } { 3 }$

• Find a common denominator.

• To add the fractions together, start by finding the least common multiple of $3$ and $10$. Then use that number as a common denominator. This table lists multiples of $3$ and $10$.
$\left. \begin{array} { | c | c | c | c | c | c | c | } \hline 3 & { 6 } & { 9 } & { 12 } & { 15 } & { 18 } & { 21 } & { 24 } & { 27 } & { 30 } & { 33 } \\ \hline 10 & { 20 } & { 30 } & { 40 } & { 50 } & { 60 } & { 70 } & { 80 } & { 90 } & { 100 } & { 110 } \\ \hline \end{array} \right.$

• LCM is $30$. Rewrite each fraction to have a denominator of $30$ by using Giant Ones, as shown below. Can you add the fractions now?
$\frac{7}{10}\cdot$ $+\ \frac{2}{3}\cdot$ $=\frac{21}{30}+\frac{20}{20}$

• $\frac{41}{30}\text{ or }1\frac{11}{30}$

1. $0.9−0.04$

Whenever adding or subtracting decimals, be sure to line up the decimal points! It may help to write this problem like this:
$\begin{array}{r} 0.90 \\ -0.04\\ \hline \; ? \; ? ? \end{array}$

Also, remember that the decimal point will fall in the same place in your answer.

1. $3 \frac { 1 } { 4 } + 2 \frac { 11 } { 12 }$

$3\frac{1}{4} = \frac{12}{4}+\frac{1}{4}=\frac{13}{4}$. Rewrite $2 \frac { 11 } { 12 }$ as a fraction greater than one. Then follow the example in Part (a).

1. $14\frac{1}{3}-9\frac{1}{5}$

• $14\frac{1}{3}-9\frac{1}{5}=\frac{43}{3}-\frac{46}{5}=\frac{5}{5}\cdot\frac{43}{3}-\frac{3}{3}\cdot\frac{46}{5}=\frac{?}{15}-\frac{?}{15}=\frac{?}{15}$