Question

Mid chapter checkpoint 5th grade chapter 6 awser key

Answer 1

QUESTION 1

A common multiple is a number that is a multiple of two or more numbers.

For instance 18 is a common multiple of 2 and 3.

This is not the only common multiple.

QUESTION 2

A common denominator is a common multiple of two or more denominators.

For instance a common denominator for $\frac{1}{2} ,\frac{1}{4}$

is 4

This is also not the only common denominator.

QUESTION 3

We were given;

$\frac{8}{9}+\frac{4}{7}$

We want to estimate the sum of the given fractions.

We collect LCM to obtain,

$=\frac{8\times 7+9\times4}{63}$

We multiply out in the numerator to obtain,

$=\frac{56+36}{63}$

We perform the addition in the numerator to obtain,

$=\frac{92}{63}$

We express the final answer as a mixed number to obtain,

$=1\frac{29}{63}$

QUESTION 4

The given expression is $3\frac{2}{5}-\frac{5}{8}$.

Let us change the first first mixed number into an improper fraction to get,

$=\frac{17}{5}-\frac{5}{8}$

We collect LCM of the denominators which is 40 to obtain,

$=\frac{8\times17-5\times5}{40}$

We now multiply out in the numerator to get,

$=\frac{136-25}{40}$

We carry out the subtraction in the numerator to get,

$=\frac{111}{40}$

We express the final answer as a mixed number to obtain;

$=2\frac{31}{40}$

QUESTION 5

The given fraction is $1\frac{5}{6}+2\frac{2}{11}$.

Let us first of all change each mixed number to improper fractions

$=\frac{11}{6}+\frac{24}{11}$

We now collect LCM of the denominators to obtain,

$=\frac{11\times11+24\times6}{66}$

We multiply in the numerator to get,

$=\frac{121+144}{66}$

This gives,

$=\frac{265}{66}$

$=4\frac{1}{66}$

QUESTION 6

The given fractions are;

$\frac{1}{6},\frac{1}{9}$.

The least common denominator is $18$.

We obtain the equivalent fraction by multiplying the denominator and numerator of each fraction by a common factor that gives 18 in the denominator.

$\frac{1\times3}{6\times3},\frac{1\times2}{9\times2}$.

This gives us;

$\frac{3}{18},\frac{2}{18}$.

QUESTION 7

The given fractions are;

$\frac{5}{6},\frac{3}{8}$.

The least common denominator is $24$.

We obtain the equivalent fraction by multiplying the denominator and numerator of each fraction by a common factor that gives 24 in the denominator.

$\frac{5\times4}{6\times4},\frac{3\times3}{8\times3}$.

This gives us;

$\frac{20}{24},\frac{9}{24}$.

QUESTION 8

The given fractions are;

$\frac{3}{8},\frac{3}{10}$.

The least common denominator is $40$.

We obtain the equivalent fraction by multiplying the denominator and numerator of each fraction by a common factor that gives 40 in the denominator.

$\frac{3\times5}{8\times5},\frac{3\times4}{10\times40}$.

This gives us;

$\frac{15}{40},\frac{12}{40}$.

QUESTION 9

The given fractions are;

$\frac{2}{5},\frac{1}{10}$.

The least common denominator is $10$.

We obtain the equivalent fraction by multiplying the denominator and numerator of each fraction by a common factor that gives 10 in the denominator.

$\frac{2\times2}{5\times2},\frac{1\times1}{10\times1}$.

This gives us;

$\frac{4}{10},\frac{1}{10}$.

QUESTION 10

The given fractions are;

$\frac{1}{9},\frac{5}{12}$.

The least common denominator is $36$.

We obtain the equivalent fraction by multiplying the denominator and numerator of each fraction by a common factor that gives 36 in the denominator.

$\frac{1\times4}{9\times4},\frac{5\times3}{12\times3}$.

This gives us;

$\frac{4}{36},\frac{3}{36}$.

QUESTION  11

The given fractions are;

$\frac{1}{3},\frac{2}{7}$.

The least common denominator is $21$.

We obtain the equivalent fraction by multiplying the denominator and numerator of each fraction by a common factor that gives 21 in the denominator.

$\frac{1\times7}{3\times7},\frac{2\times3}{7\times3}$.

This gives us;

$\frac{7}{21},\frac{6}{21}$.

QUESTION 12,

The given fraction is

$\frac{11}{18}-\frac{1}{6}$

The least common denominator is $18$.

We collect LCD to obtain,

$=\frac{11-3\times1}{18}$

This simplifies to;

$=\frac{11-3}{18}$

$=\frac{8}{18}$

$=\frac{9}{4}$

QUESTION 13

The given fraction is

$\frac{2}{7}+\frac{2}{5}$

The least common denominator is $35$.

We collect LCD to obtain,

$=\frac{2\times5+2\times7}{35}$

This simplifies to;

$=\frac{10+14}{35}$

$=\frac{24}{35}$

QUESTION 14

The given fraction is

$\frac{3}{4}-\frac{3}{10}$

The least common denominator is $20$.

We collect LCD to obtain,

$=\frac{3\times5-3\times2}{20}$

This simplifies to;

$=\frac{15-6}{20}$

$=\frac{9}{20}$