Multiplying and Dividing by 6 and 7 Methods

Multiplying and Dividing by 6 and 7

When you multiply or divide a number by either six or seven, certain patterns emerge that can help you better understand the process and solve word problems involving these operations more effectively. Here's what you need to know about multiplying and dividing by 6 and 7.

Word Problems Involving Multiplication and Division By 6 and 7

Word problems often involve multiplication and division with various factors, including 6 and 7. To solve these problems, you need to understand the properties of these numbers. For example, 6 is divisible by 1, 2, 3, and itself, while 7 is divisible by 1 and itself. This means that if you're dividing by 6 or 7, you'll often end up with a whole number and a fraction.

Here's an example problem:

"Barry's group of friends is made up of 6 members. If each member has 5 friends, how many friends does Barry have?"

To solve this problem, you need to multiply the number of friends each member has by the number of members in the group. This gives you a total of 6 × 5 = 30 friends. Therefore, Barry has 30 friends.

Multiplying by 6

Multiplying by 6 can be done by the rule of sixes: if you multiply a number by 6, you can add that number to itself and multiply the result by 2. For example, to multiply 4 by 6, you would add 4 to itself and multiply 8 by 2, resulting in 16.

You can also multiply by 6 by multiplying by 2 and then multiplying by 3. For example, to multiply 5 by 6, you would multiply 5 by 2 to get 10 and then multiply 10 by 3 to get 30.

Dividing by 6

Dividing by 6 can be done by the rule of sixes as well. If you divide a number by 6, you can subtract that number from itself and divide the result by 2. For example, to divide 24 by 6, you would subtract 24 from itself and divide 48 by 2, resulting in 12.

You can also divide by 6 by dividing by 2 and then dividing by 3. For example, to divide 42 by 6, you would divide 42 by 2 to get 21 and then divide 21 by 3 to get 7.

Multiplying by 7

Multiplying by 7 can be done by multiplying by 1 and then multiplying by 7. For example, to multiply 8 by 7, you would multiply 8 by 1 to get 8 and then multiply 8 by 7 to get 56.

You can also multiply by 7 by multiplying by 10 and then multiplying by 3. For example, to multiply 12 by 7, you would multiply 12 by 10 to get 120 and then multiply 120 by 3 to get 360.

Dividing by 7

Dividing by 7 can be done by dividing by 1 and then dividing by 7. For example, to divide 14 by 7, you would divide 14 by 1 to get 14 and then divide 14 by 7 to get 2.

You can also divide by 7 by dividing by 10 and then dividing by 3. For example, to divide 49 by 7, you would divide 49 by 10 to get 4.9 and then divide 4.9 by 3 to get 1.63.

By understanding these patterns and rules, you can solve word problems involving multiplication and division by 6 and 7 more efficiently and accurately. Practice using these methods to strengthen your understanding and improve your problem-solving skills.