{"id":267,"date":"2024-04-01T14:07:01","date_gmt":"2024-04-01T13:07:01","guid":{"rendered":"https:\/\/tutors4you.com\/?page_id=267"},"modified":"2024-04-01T14:07:03","modified_gmt":"2024-04-01T13:07:03","slug":"tutorial-on-fractions","status":"publish","type":"page","link":"https:\/\/tutors4you.com\/index.php\/tutorial-on-fractions\/","title":{"rendered":"Tutorial on Fractions"},"content":{"rendered":"\n\n\t\t
\n\t\t\t\n\t\t\t

1\/2, 3\/4, 4\/10 are fractions. The numbers on\n top are called numerators. These are the numbers 1, 3 and\n 4. The numbers below are called denominators. These are\n the numbers 2, 4 and 10.<\/font><\/p>\n

The denominator gives how many equal parts\n are there. The numerator represents how many of these are\n taken.<\/font><\/p>\n

The denominator cannot be 0. For example 1\/0\n is not allowed. This is so as division by 0 is not\n defined.<\/font><\/p>\n

However, 0\/1 is allowed and is equal to 0. <\/font><\/p>\n

If numerator and denominator are the same\n the fraction becomes equal to 1. For example:<\/font><\/p>\n

2\/2=1 and 9\/9=1<\/font><\/p>\n

We can also have fractions like 10\/2=5 and\n 18\/6=3.<\/font><\/p>\n

Mixed Numbers
\n <\/u>These numbers are made up of a whole number and a\n fraction. For example:<\/font><\/p>\n

5 1\/2 is a mixed number and is equal to 5 +\n 1\/2.<\/font><\/p>\n

A mixed number may be changed into fraction\n through the following steps:<\/font><\/p>\n

Step 1
\n <\/u>Multiply the whole number and the denominator of the\n fraction part.<\/font><\/p>\n

For example in 5 1\/2 we multiply 5 and 2 to\n get 10.<\/font><\/p>\n

Step 2
\n <\/u>To the result of Step 1 add the numerator of the\n fraction part.<\/font><\/p>\n

In our example the numerator of the fraction\n part 1\/2 is 1. So 10 + 1 = 11.<\/font><\/p>\n

Step 3
\n <\/u>Write the result of Step 2 as the numerator and the\n denominator of the fraction part as the denominator.<\/font><\/p>\n

In our exampls we get 11\/2.<\/font><\/p>\n

So 11\/2 = 5 1\/2 which shows that we can\n change a fraction where the numerator is greater than the\n denominator into a mixed number. For doing this follow\n these steps:<\/font><\/p>\n

Step 1
\n <\/u>Divide the numerator by the denominator and obtain\n the remainder. <\/font><\/p>\n

In our example 11\/2, 2 goes 5 times into 11\n leaving a remainder of 1.<\/font><\/p>\n

as 2 x 5 = 10
\n and 11 – 10 = 1<\/font><\/p>\n

Step 2
\n <\/u>The remainder over the denominator gives us the\n fractional part. So we get.<\/font><\/p>\n

11\/2 = 5 1\/2<\/font><\/p>\n

Whole Numbers and Mixed Numbers
\n <\/u>12\/3 = 4 0\/3 = 4<\/font><\/p>\n

Here 0\/3 is obviously = 0 hence 4 0\/3 = 4.<\/font><\/p>\n

However representing 4 as 12\/3 is useful at\n times. We need to do this when we do calculations between\n whole numbers and fractions.<\/font><\/p>\n

Multiplication of Fractions
\n <\/u>Say we want to multiply 3\/4 with 5\/6. <\/font><\/p>\n

We do this by multiplying 3 x 5 which gives\n us the result 15, which is the numerator of the result.\n Similarly 4 x 6 gives the result 24 which is the new\n denominator. We can write this multiplication as under:<\/font><\/p>\n

3\/4 x 5\/6 = (3×5) \/ (4×6) =15\/24.<\/font><\/p>\n

Dividing Fractions
\n <\/u>Say we want to divide 7\/8 by 3\/4.<\/font><\/p>\n

For this we have the following steps:<\/font><\/p>\n

Step 1
\n <\/u>Invert 3\/4, or in other words write it up side down\n with 4 as the numerator and 3 as the denominator.<\/font><\/p>\n

Step 2
\n <\/u>Now multiply this with the first fraction. That is:<\/font><\/p>\n

7\/8 x 4\/3 = (7×4) \/ (8×3) = 28\/24<\/font><\/p>\n

Reducing a Fraction to Lowest Terms
\n <\/u>Look at the two fractions given below:<\/font><\/p>\n

5\/6 and 4\/8<\/font><\/p>\n

In the first fraction 5 is a prime number.\n So its factors are 1 and 5. That is 5 = 1 x 5. However, 6\n = 1 x 2 x 3. There are no common factors (neglecting 1).\n We say that 5\/6 is already expressed in its lowest terms.<\/font><\/p>\n

In the fraction 4\/8, 4 = 2 x 2 and 8 = 2 x 2\n x 2. Here 2 x 2 is common to both 4 and 8. Hence 4\/8 can\n be written as;<\/font><\/p>\n

4\/8 = (2×2) \/ (2x2x2) = 1\/2<\/font><\/p>\n

2×2 being common to both numerator and\n denominator can be cancelled. This leaves us with 1\/2 as\n the result.<\/font><\/p>\n

By changing 4\/8 to 1\/2 we say that 4\/8 has\n been reduced to its lowest terms.<\/font><\/p>\n

The value of 4\/8 and 1\/2 is the same as\n cancelling common factors does not change the value of\n the fraction.<\/font><\/p>\n

Adding Fractions
\n <\/u>5\/16 + 7\/16 = (5+7)\/16 = 12\/16 = 3\/4<\/font><\/p>\n

Notice the denominator of 5\/16 and 7\/16 is\n the same. This has been done to aid explaining addition\n of fractions. For adding fractions follow the following\n steps:<\/font><\/p>\n

Step 1
\n <\/u>Write the common denominator.<\/font><\/p>\n

Step 2
\n <\/u>Add the numerators, which gives us 12\/16 which in its\n lowes terms is 3\/4.<\/font><\/p>\n

If the denominators of the fractions are not\n the same we have to make them so before adding the\n fractions. For example:<\/font><\/p>\n

5\/6 + 1\/4<\/font><\/p>\n

Here 6 x 2 = 12 and 4 x 3 = 12<\/font><\/p>\n

So we can re-write the fractions as:<\/font><\/p>\n

(5×2) \/ (6×2) = 10\/12 and (1×3) \/ (4×3) =\n 3\/12<\/font><\/p>\n

Then add 10\/12 + 3\/12 = (10+3)\/12 = 13\/12 =\n 1 1\/12<\/font><\/p>\n

Here 5\/6 and 10\/12 are equivalent fractions\n as they have the same value. 1\/4 and 3\/12 are also\n equivalent fractions for the same reason.<\/font><\/p>\n

Subtracting Fractions
\n <\/u>3\/4 -1\/4 = (3-1)\/4 = 2\/4 =1\/2<\/font><\/p>\n

It is similar to the steps used in adding\n fractions as explained above.<\/font><\/p>\n\t\t<\/div>\n\t\n","protected":false},"excerpt":{"rendered":"

1\/2, 3\/4, 4\/10 are fractions. The numbers on top are called numerators. These are the numbers 1, 3 and 4. The numbers below are called denominators. These are the numbers 2, 4 and 10. The denominator gives how many equal parts are there. The numerator represents how many of these are taken. The denominator cannot […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-267","page","type-page","status-publish","hentry"],"blocksy_meta":[],"yoast_head":"\nTutorial on Fractions - Tutors 4 You<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/tutors4you.com\/index.php\/tutorial-on-fractions\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Tutorial on Fractions - Tutors 4 You\" \/>\n<meta property=\"og:description\" content=\"1\/2, 3\/4, 4\/10 are fractions. The numbers on top are called numerators. These are the numbers 1, 3 and 4. The numbers below are called denominators. These are the numbers 2, 4 and 10. The denominator gives how many equal parts are there. The numerator represents how many of these are taken. 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The numbers on top are called numerators. These are the numbers 1, 3 and 4. The numbers below are called denominators. These are the numbers 2, 4 and 10. The denominator gives how many equal parts are there. The numerator represents how many of these are taken. 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