Factors & Multiples 2

What is the greatest 5-digit even number that can be formed using the digits 1, 6, 3, 7 and 9?

Tags

CCSS.4.NBT.A.2

How many hundreds are there in 12 500?

Tags

CCSS.2.NBT.A.1B

Complete the number pattern.

33 615, 32 615, 31 615, 30 615, ________

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CCSS.4.OA.C.5

What is the smallest 5-digit even number that can be formed using the digits 4, 5, 1, 2 and 8?

Joyce spent $33 on a dress and had $120 left when rounded to the nearest ten.

What was the smallest possible amount of money that she had at first?

Answer explanation

Let's break down the problem step by step.

Joyce spent $33 on a dress.

After spending $33, Joyce had $120 left when rounded to the nearest ten.

The amount left after rounding to the nearest ten is $120.

This means the actual amount of money Joyce had left could be anywhere between $115 and $124 before rounding to the nearest ten. (Because any amount in this range would round to $120 when rounded to the nearest ten.)

We need to find the smallest possible amount of money Joyce had at first.

The smallest possible amount she could have left is $115.

To find the total amount of money she had at first, we add the $33 she spent on the dress:

33 + 115 = 148

Find the sum of 1829 and 1849 when they are rounded to the nearest ten and thousand, respectively.

Answer explanation

Let's go step by step.

Rounding 1829 to the nearest ten:

The last digit of 1829 is 9, which is greater than or equal to 5, so we round up.

1829 rounded to the nearest ten is 1830.

Rounding 1849 to the nearest thousand:

The hundreds digit of 1849 is 8, which is greater than or equal to 5, so we round up.

1849 rounded to the nearest thousand is 2000.

Now, let's find the sum of these rounded numbers:

1830 + 2000 = 3830

A number is between 30 and 40.

It is also a multiple of 4.

When it is divided by 8, there is no remainder.

What is the number?

Answer explanation

Let's break down the conditions:

The number is between 30 and 40.

So, the possible numbers are: 31, 32, 33, 34, 35, 36, 37, 38, 39.

It is a multiple of 4.

We need to find which of the numbers between 30 and 40 are multiples of 4.

The multiples of 4 in this range are: 32, 36.

When it is divided by 8, there is no remainder.

This means the number must also be a multiple of 8. We check the numbers from the previous step:

32 ÷ 8 = 4

32÷8=4 (no remainder)

36 ÷ 8 = 4.5

36÷8=4.5 (remainder exists)

Conclusion:

The number that meets all the conditions is 32.

Tags

CCSS.5.NBT.A.2

Nicholas’ age this year is a multiple of 3.

He is less than 30 years old but older than 10 years old.

Next year, his age will be a multiple of 5.

How old is Nicholas this year?

Answer explanation

Let's break this down step by step:

Nicholas' age this year is a multiple of 3 and less than 30.

The multiples of 3 that are less than 30 are: 3, 6, 9, 12, 15, 18, 21, 24, 27.

Next year, his age will be a multiple of 5.

This means if we add 1 to his age, it should be a multiple of 5.

Let's check each of the possible ages and see if adding 1 results in a multiple of 5:

3 + 1 = 4 (not a multiple of 5)

6 + 1 = 7 (not a multiple of 5)

9 + 1 = 10 (a multiple of 5)

12 + 1 = 13 (not a multiple of 5)

15 + 1 = 16 (not a multiple of 5)

18 + 1 = 19 (not a multiple of 5)

21 + 1 = 22 (not a multiple of 5)

24 + 1 = 25 (a multiple of 5)

27 + 1 = 28 (not a multiple of 5)

From this, we see that 9 and 24 both meet the condition.

Conclusion:

Nicholas could either be 9 or 24 years old this year.

A certain number is between 55 and 65.

It is also a common multiple of 5 and 6.

What is the number?

Answer explanation

Let's break this down:

The number is between 55 and 65.

So, the possible numbers are: 56, 57, 58, 59, 60, 61, 62, 63, 64.

It is a common multiple of 5 and 6.

To find the common multiple of 5 and 6, we need to find the least common multiple (LCM) of 5 and 6. The LCM of 5 and 6 is 30.

Now, we need to check the multiples of 30 that fall between 55 and 65. The first multiple of 30 is 30, the second is 60, and the next one is 90, which is outside the range.

Therefore, the number is 60.

What is the sum of the first 4 multiples of 9?

Answer explanation

The first 4 multiples of 9 are:

9 × 1 = 9

9 × 2 = 18

9 x 3 = 27

9 × 4 = 36

Now, let's find their sum:

9 + 18 + 27 + 36 = 90

So, the sum of the first 4 multiples of 9 is 90.