Download Every Fraction Can Be Written As a Decimal

1.Make sure your fractions have a common denominator. If they don’t have one, find
one.
1/5 + 2/5—These fractions are ready to add because they have the same
denominator.
½ +2/3—You need to find a common denominator before you can add these.
2.Then add (or subtract) across the numerators and keep the same denominator.
1+2
5
3
5
So 1/5+2/5=3/5.
What happens when the numerator is bigger than
the denominator?
A fraction with a numerator that is larger than the denominator is called an improper
fraction. These are fractions that are larger than one. When might you get a fraction
larger than one?
Moving from Improper Fractions to Mixed
Numbers
Often, the improper fraction will be easier to think about if you change it to a mixed
number. A mixed number is a combination of a whole number and a proper fraction: 1
1/3, 2 ½, etc.
1.Subtract a fraction equal to 1 from the improper fraction:
3/2-2/2=1/2
2.Sometimes you will have to do this more than once. Keep track of how many times you subtract one
because this will become your whole number in the mixed number.
3.Then rewrite the fraction as the whole number you subtracted with the remaining fraction beside it.
3/2= 1 ½
What is a Decimal?
A decimal is like a fraction because it is a number between 0 and 1.
0.1
0.25 0.5
0.95
Decimals are often added to whole numbers by joining them to the whole number with a
decimal point.
1.1
2.25 4.5
6.95
Decimals are fractions.
Decimals are fractions with denominators of 10, 100, 1000, and other powers of 10.
0.1=1/10
0.25= 25/100
0.5= 5/10
0.95=95/100
To write a decimal as a fraction find the place value of the last digit of the decimal. That
number will be the denominator. Then write the digits in the decimal over the
denominator.
Place Value with Decimals
Thousands
Hundreds
Tens
Ones
Tenths
Hundredths
Thousandths
1
2
3
4
5
6
7
This number would be read:
One thousand two hundred thirty four and five hundred sixty seven thousandths.
Rules for Reading Decimals
1.Always use “and” between the whole number and the decimal to show where the
decimal point is. (Never say “and” when you are reading a number without a decimal.)
2.The decimal always has the name of the last digit’s place value even if there are nonzero digits in the other places. For example, if the last digit is in the tenths place, the
decimal is in tenths. If the last digit is in the thousandths place, the decimal is in
thousandths.
Every Fraction Can Be Written As a Decimal
Do you remember what we did to find common denominators of fractions?
To write a fraction as a decimal, most of the time you can find a common denominator that is a power of 10
(10, 100, 1000, 10,000, etc.) and multiply each fraction by a fraction equivalent to 1 to get the new fraction
with the new denominator.
Then write the new fraction as a decimal.
How do we write ½ as a decimal?
1.List multiples of 2 and find one that is a power of 10.
2, 4, 6, 8, 10
2.Multiply the numerator and denominator of ½ each by 5 to get the fraction in the new denominator.
1x5
5
2x5
10
3.Then write the numerator of the fraction in the appropriate place values in the decimal.
5/10=0.5
Writing Fractions as Decimals
Sometimes, the denominator of a fraction will never have a multiple that is also a power
of 10. This happens with 1/3. In these cases, you have to divide the numerator by the
denominator to find the decimal.
Writing zeros after the decimal point doesn’t, change the number, but it makes it so that we can divide 3 into what
looks like 10. Act as if the numbers are whole numbers and complete the division, but remember to raise the decimal
point to the answer line.
Repeating Decimals
As we saw when we tried to write 1/3 as a decimal, some decimals keep repeating
forever. These decimals are called repeating decimals. Because we can’t keep writing
the pattern forever, we write a bar over the part of the decimal that repeats to show that it
is a repeating decimal.
1/3=0.33
Summary
•A fraction is part of a whole, part of a collection, and a point on a number line.
•Before adding, subtracting, or comparing fractions, you must have a common
denominator.
•Decimals are fractions with denominators that are powers of 10: 10, 100, 1000, etc.
•All fractions can be written as decimals.