Fractions and Decimals Relationship

10 Questions

Match the following equivalent fractions:

$\frac{2}{3}$ = $\frac{8}{12}$ $\frac{7}{10}$ = $\frac{21}{30}$ $\frac{5}{6}$ = $\frac{15}{18}$ $\frac{4}{9}$ = $\frac{12}{27}$

Match the following fractions with their sum after adding:

$\frac{1}{5}$ and $\frac{2}{5}$ = $\frac{3}{10}$ $\frac{2}{7}$ and $\frac{3}{14}$ = $\frac{5}{14}$ $\frac{3}{9}$ and $\frac{4}{9}$ = $1$ $\frac{1}{3}$ and $\frac{2}{6}$ = $1$

Match the following fractions that are greater in value:

$\frac{5}{8}$ = $\frac{4}{7}$ $\frac{2}{5}$ = $\frac{3}{8}$ $\frac{7}{11}$ = $\frac{6}{9}$ $\frac{1}{4}$ = $\frac{2}{9}$

Match the following fractions with their equivalent decimal form:

$\frac{3}{4}$ = $0.75$ $\frac{5}{9}$ = $0.555...$ $\frac{2}{11}$ = $0.181818...$ $\frac{7}{20}$ = $0.35$

Match the following fractions in descending order of value:

$\frac{4}{5}$ = $0.80$ $\frac{2}{3}$ = $0.666...$ $\frac{11}{15}$ = $0.733...$ $\frac{3}{7}$ = $0.428571...$

Match the following fractions with their equivalent decimal representation:

$\frac{3}{5}$ = 0.6 $\frac{2}{3}$ = 0.666... $\frac{4}{7}$ = 0.5714 $\frac{5}{8}$ = 0.625

Match the following fractions with their equivalent fractions that have a common denominator of 20:

$\frac{3}{4}$ = $\frac{15}{20}$ $\frac{7}{10}$ = $\frac{14}{20}$ $\frac{2}{5}$ = $\frac{8}{20}$ $\frac{1}{3}$ = $\frac{6}{20}$

Match the following fractions with the correct statement about which is greater or if they are equal:

$\frac{2}{3}$ and $\frac{3}{5}$ = $\frac{2}{3} > \frac{3}{5}$ $\frac{5}{8}$ and $\frac{7}{10}$ = $\frac{7}{10} > \frac{5}{8}$ $\frac{1}{4}$ and $\frac{3}{8}$ = $\frac{1}{4} = \frac{3}{8}$ $\frac{9}{12}$ and $\frac{2}{3}$ = $\frac{2}{3} > \frac{9}{12}$

Match the following statements with the correct method of converting a fraction to a decimal or vice versa:

Converting fraction to decimal involving division = $\frac{2}{5} = 0.4$ Converting decimal to fraction by multiplying with powers of ten = $0.125 = \frac{125}{1000}$

Match the following fractions with their equivalent fractions that have a common denominator of 100:

$\frac{1}{4}$ = $\frac{25}{100}$ $\frac{3}{5}$ = $\frac{60}{100}$ $\frac{7}{8}$ = $\frac{87.5}{100}$ $\frac{9}{10}$ = $\frac{90}{100}$

Study Notes

Fractions and Decimals

Fractions and decimals are two different ways of representing parts of a whole number. While they may seem like separate concepts at first glance, there is actually quite a bit of overlap between them. In this article, we will explore the relationship between these two representations by looking at their equivalence, addition, comparison, and conversion from one form to another.

Equivalent Fractions

Equivalent fractions are fractions that represent the same value. For example, both (\frac{1}{2}) and (\frac{2}{4}) are equal because both halves make up a whole. This concept can be extended to other values, such as (\frac{9}{18} = \frac{3}{6}), where each part represents the same portion of the whole when compared against its denominator. This idea of proportionality underlies the concept of equivalent fractions and is a key principle when working with them.

Adding Fractions

Adding fractions usually involves finding their least common denominator (LCD). The LCD is the smallest number that can be divided evenly by all denominators involved. For instance, if you want to add (\frac{1}{4}) and (\frac{3}{8}), you would multiply both by (2) so they have a common denominator of (8). This gives (\frac{2}{8} + \frac{6}{8} = \frac{8}{8} = 1), which makes sense since if you multiply (2) by (3) and divide it into four quarters, you get eight pieces of equal size.

Comparing Fractions

Comparing fractions is a matter of determining which one has more or fewer parts relative to the whole. For instance, (\frac{3}{4}) is bigger than (\frac{1}{2}) because three out of every four parts makes up more of the whole than half of four parts does. Similarly, (\frac{9}{10}) is less than (1) since it represents nine tenths rather than all ten parts.

Fraction to Decimal Conversion

Converting fractions to decimals involves dividing the numerator by the denominator. For example, (\frac{7}{10}) divided by (10) gives (0.7). Conversely, converting decimals to fractions requires multiplying the decimal by some power of ten until it becomes an integer. For example, (0.5) multiplied by (10) yields (5,\text{ so } \frac{5}{10} = \frac{1}{2}).

In summary, fractions and decimals both help us understand parts of a whole, with equivalent fractions being represented by the same value. Adding fractions often involves finding a common denominator while comparing them means understanding how many parts each has compared to the whole. Finally, converting between fractions and decimals simply involves division and multiplication by powers of ten respectively.