How do I add and subtract fractions with different denominators? This is a common question among students learning about fractions. Fractions with different denominators can be challenging to work with, but with the right approach, you can easily add and subtract them. In this article, we will guide you through the process step by step, so you can confidently tackle these problems in your math assignments.
In order to add or subtract fractions with different denominators, you first need to find a common denominator. The common denominator is the smallest number that both denominators can divide into evenly. To find the common denominator, you can use the least common multiple (LCM) of the two denominators.
Here’s how to find the LCM:
1. List the multiples of each denominator.
2. Identify the smallest multiple that appears in both lists.
For example, if you have the fractions 1/3 and 1/4, you would list the multiples of 3 (3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120) and the multiples of 4 (4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228, 232, 236, 240, 244, 248, 252, 256, 260, 264, 268, 272, 276, 280, 284, 288, 292, 296, 300, 304, 308, 312, 316, 320, 324, 328, 332, 336, 340, 344, 348, 352, 356, 360, 364, 368, 372, 376, 380, 384, 388, 392, 396, 400, 404, 408, 412, 416, 420, 424, 428, 432, 436, 440, 444, 448, 452, 456, 460, 464, 468, 472, 476, 480, 484, 488, 492, 496, 500, 504, 508, 512, 516, 520, 524, 528, 532, 536, 540, 544, 548, 552, 556, 560, 564, 568, 572, 576, 580, 584, 588, 592, 596, 600, 604, 608, 612, 616, 620, 624, 628, 632, 636, 640, 644, 648, 652, 656, 660, 664, 668, 672, 676, 680, 684, 688, 692, 696, 700, 704, 708, 712, 716, 720, 724, 728, 732, 736, 740, 744, 748, 752, 756, 760, 764, 768, 772, 776, 780, 784, 788, 792, 796, 800, 804, 808, 812, 816, 820, 824, 828, 832, 836, 840, 844, 848, 852, 856, 860, 864, 868, 872, 876, 880, 884, 888, 892, 896, 900, 904, 908, 912, 916, 920, 924, 928, 932, 936, 940, 944, 948, 952, 956, 960, 964, 968, 972, 976, 980, 984, 988, 992, 996, 1000) and identify that 12 is the smallest multiple that appears in both lists.
Once you have found the common denominator, you can rewrite the fractions with the new denominator. To do this, multiply the numerator and denominator of each fraction by a number that will make the denominator equal to the common denominator.
For example, to add 1/3 and 1/4, you would rewrite the fractions as follows:
1/3 = (1 4) / (3 4) = 4/12
1/4 = (1 3) / (4 3) = 3/12
Now that both fractions have the same denominator, you can add or subtract the numerators and keep the denominator the same:
4/12 + 3/12 = 7/12
And that’s how you add fractions with different denominators. To subtract fractions, follow the same steps, but subtract the numerators instead of adding them:
4/12 – 3/12 = 1/12
Remember, the key to adding and subtracting fractions with different denominators is to find a common denominator and then rewrite the fractions with that denominator before performing the operation. With practice, you’ll be able to do this quickly and easily.
